46 + Interview Questions in SETS-AND-RELATIONS IN GENERAL AWARENESS Page 1 InterviewSolution

1.	If `C subY` and `Y subX`, then_____
Answer» Correct Answer - X=Y

Discussion

2.	If `P=(1,2,3,4,5,6,7)` and `Q=(2,5,8,9)`, then find `P cup Q`.
Answer» Correct Answer - (1,2,3,4,5,6,7,8,9)

Discussion

3.	Consider the following statements. `p:3 in(1,(3),5,7)` `q, 2 in(1,(3,4),4)` Which of the following is true?A. p aloneB. q aloneC. Both p and qD. Neither p nor q.
Answer» Correct Answer - D Recall that x and (x) are different.

Discussion

4.	If A=(1,2,3), then the relation R={(1,1)(2,2),(3,1),(1,3)}` isA. reflexive.B. symmetricC. transitive.D. equivalence.
Answer» Correct Answer - B Use the definition of reflexive, symmetric and transitive.

Discussion

5.	If `A={n:(n^(3)+5n^(2)+2)/(n)` is an integer and n itself is an integer}, then the number of elements in the set A isA. 1B. 2C. 3D. 4
Answer» Correct Answer - D List out value of n, such that 2/n is an integer.

Discussion

6.	If `A=(1,2,3)` and `B=(2,6,7)`, then `(A-B)cup(B-A)=`A. `phi`B. `mu`C. `(1,2,3,6,7)`D. `(1,3,6,7)`
Answer» Correct Answer - D `x in A -BrArr x in A` and `x cancelin B`.

Discussion

7.	Which of the following cannot be the cardinal number of the power set of any finite set?A. 26B. 32C. 8D. 16
Answer» Correct Answer - A Required answer cannot be expressed in the form of `2^(n),n in w`.

Discussion

8.	If `n(A)=8` and `n(B)=6` and the sets A and B are disjoint, then find `n(AcupB)`.
Answer» Given, `n(A)=B` and `n(B)=6,A` and B are disjoint `rArr AcapB=phirArrn(AcapB)=0`. `therefore n(AcupB)=n(A)+n(B)-n(AcapB)=8+6-0=14`.

Discussion

9.	The cardinal number of a set is 5. find the cardinal number of the power set.
Answer» Correct Answer - 32

Discussion

10.	A relation `R:Zrarr2` is such that `R={(x,y)//y=2x+1)` is aA. one to one relation.B. many to one relation.C. one to many relation.D. many to many relation.
Answer» Correct Answer - A Recall one-one relation.

Discussion

11.	If (x-y,x+y)=(2,8), then the values of x and y are respectively.A. 5,3B. 7,5C. 4,2D. 10,8
Answer» Correct Answer - A If `(x,y)=(a,b)`, then x=a and y=b.

Discussion

12.	Let Z denote the set of integers, then `(x in Z,\|x-3\|lt4cap{x inZ:\|x-4\|lt5}`=A. {-1,0,1,2,3,4}B. {-1,0,1,2,3,4,5}C. {0,1,2,3,4,5,6}D. {-1,0,1,2,3,5,6,7,8,9}
Answer» Correct Answer - C `\|x\|ltarArr-altxlta`.

Discussion

13.	If `n(P)=2` and `n(Q)=5000,` then `n(PxxQ)=`______
Answer» Correct Answer - 10000

Discussion

14.	In `n(AcupB)=16` and `n(AcapB)=4`, then the number of elements in the symmetric difference of A and B is_____
Answer» Correct Answer - 12

Discussion

15.	If A=(1,2,3,4) then how many subsets of A contain the elements 3?A. 24B. 28C. 8D. 16
Answer» Correct Answer - C The number of subsets of A containing one particular element is `2^(n-1)`.

Discussion

16.	If `X=(x:x^(2)-12x+20=0)` and `Y=(x:x^(2)+5x-14=0)` , then X-Y=A. `(2)`B. `(10)`C. `(-7)`D. `()`
Answer» Correct Answer - B Solve the two equations for x then write X and Y. Now find X-Y.

Discussion

17.	If `n(mu)=100,n(A)=50,n(B)=20` and `n(A cap B)`=10, then `n[(AcupB)]=`A. 60B. 30C. 40D. 20
Answer» Correct Answer - C (i) `n(AcupB)=n(mu)-(AcupB)` (ii) `n(AcupB)=n(A)+n(B)-n(AcapB)`. (iii) `n[(AcupB)^(C)]=n(mu)-n(AcupB)`.

Discussion

18.	If P and Q are disjoint, then P-Q=______ and Q-P=_________
Answer» Correct Answer - P,Q

Discussion

19.	The number of subsets of ` A xx B` if n(A)=3 and n(B)=3 isA. 512B. 256C. 511D. 235
Answer» Correct Answer - A Number of subsets`=2^(n-1)`

Discussion

20.	If `P=(a,b,c,d)` and `Q=(1,2,3,4,5)` then `n(PxxQ)`=________
Answer» Correct Answer - 20

Discussion

21.	If `n(AxxB)` =45, then n(A) cannot beA. 15B. 17C. 5D. 9
Answer» Correct Answer - B n(A) is a factor of `n(AxxB)`.

Discussion

22.	If `P_(n)` is the set of first n prime numbers, then `underset(n=3)overset(10)capP_(n)` isA. {3,5,7,11,13,17,19}B. {2,3,5}C. {2,3,5,7,11,13,17}D. {3,5,7}
Answer» Correct Answer - B (i) Recall the definition of intersection of sets and subsets. (ii) If `AsubB`, then `AcapB=A`. (iii) `underset(n=1)overset(10)(cap)P_(n)=p_(3)capp_(4)cap. . . .capp_(10)=p_(3)`.

Discussion

23.	A relation `R,NrarrN` defined by `R={(x,y)//y=x^(2)+1)` isA. one to oneB. one to manyC. many to oneD. many to many.
Answer» Correct Answer - A (i) Write some elements of R and then check. (ii) (2,3) and (-2,3) are the two elements of R. (iii) Now check which type of relation is

Discussion

24.	If V=(a,e,i,o,u), then find the number of non empty proper subsets of V.
Answer» Correct Answer - 30

Discussion

25.	If `n(A)=6` and n(B)=3, then find the number of subsets of `A xx B`.
Answer» Correct Answer - `2^(18)`

Discussion

26.	If `R={(a,b)//\|a+b\|=\|a\|+\|b\|}` is a relation on a set `{-1,0,1}` then R is_A. reflexiveB. symmetricC. anti symmetricD. equivalence.
Answer» Correct Answer - D (i) Write all the element of R. (ii) R={(0,0),(1,1),(-1,-1),(0,-1),(-1,0),(1,0),(0,1)} (iii) Check the properties , which R satisfy

Discussion

27.	If A={`p in N,p` is a prime and `p=(7n^(2)+3n+3)/(n)` for some `n in N`), then the number of elements in the set A isA. 1B. 2C. 3D. 4
Answer» Correct Answer - A Substitute n=1 and n=3.

Discussion

28.	If `A=(1,2)` and B=(2,3), then find the number of elements in `(AxxB)cap(BxxA)`. The following are the steps involved in solving the above problem. Arrange them in sequential order. (A) `(AxxB)cap(BxxA)=(2,2)` (B) Given `A=(1,2)` and B=(2,3) (C) `n[)AxxB)cap(BxxA)]=1` (D) `AxxB={(1,2)(1,3)(2,2)(2,3)}` and `B xxA={(2,1),(2,2),(#,1),(3,2)}`A. BADCB. BDCAC. BCADD. BDAC
Answer» Correct Answer - D The sequential order is CABD.

Discussion

29.	If `R={(a,b)//\|a+b\|=a+b}` is a relation defined on a set (-1,0,1) then R is____A. reflexiveB. symmetricC. anti symmetricD. transitive.
Answer» Correct Answer - B (i) Verify the reflexive symmetric and transitive properties of relations. (ii) R={(0,0),(1,1),(1,-1),(01,1),(0,1),(1,0)}. (iii) Check which properties does R satisfy

Discussion

30.	The number of subsets of `{(a),(b,c),d,e)` is _____A. 32B. 16C. 8D. 20
Answer» Correct Answer - B Let `A={(a),(b,c),(d,c)}rarrn(A)=4` `therefore` The number of subsets of `A=2^(4)=16`.

Discussion

31.	A relation R: `ZrarrZ` defined by `R={(x,y)//y=x^(2)-1}` isA. one to one relation.B. many to one relation.C. many to many relationD. many to many relation.
Answer» Correct Answer - B (i) Write some possibilities of (X,y) (ii) (2,3) and (-2,3) are th two elements of R. (iii) Now, check which type of relation is R.

Discussion

32.	Example of an equivalence relation among the following isA. is a father ofB. is less thanC. is congruent toD. is an uncle of
Answer» Correct Answer - C Use the definition of reflexive, symmetric and transitive.

Discussion

33.	The relation is not equal to is defined on the set of real numbers is satisfies which of the following?A. Reflexive onlyB. Symmetric onlyC. Transitive onlyD. equivalence.
Answer» Correct Answer - B Recall the definitions of reflexvie symmetric and transitive relation.

Discussion

34.	R and S are two sets such that n(R)=7 and R `cap` S`nephi` Further n(S)=6 and S `DeltaR`. The greatest. Possible value of `n(R DeltaS)` is____A. 11B. 12C. 13D. 10
Answer» Correct Answer - A (i) Recall all the concept of symmetrical difference. (ii) For the greatest possible value of `n(RDeltaS)` `n(RcapS)` is minimum. (iii) As `R capSnephi,n(RcapS)=1`. (iv) `n(R DeltaS)=n(R cupS)-n(RcapS)`.

Discussion

35.	If `R={(a,a),(a,c),(b,c),(b,b),(c,c),(a,b)}` on the set `X=(a,b,c)`, then how many subsets of R are reflexive relations?A. 15B. 16C. 8D. 9
Answer» Correct Answer - C Given `R={(a,b),(a,c),(b,c),(b,b),(c,c),(a,b)}` `therefore` The number of reflexive relations =The number of subsets formed by the elements (a,c),(b,c) and (a,b)`=2^(3)=8`.

Discussion

36.	Consider the following statements: (i) Every reflexive relation is anti-symmetric. (ii) Every symmetric relation is anti-symetric which among i and ii is true?A. i alone is trueB. ii alone is trueC. Both i and ii are trueD. Neither i nor ii is true.
Answer» Correct Answer - D Recall the definition of reflexive, symmetric, antisymmetric transitive relations.

Discussion

37.	If a set A has 13 elements and R is a reflexive relation on A with a elementss, ` n in Z^(+)`, thenA. `13lenle26`B. `0lenle26`C. `13lenle169`D. `0lenle169`
Answer» Correct Answer - C (i) Recall the properties of identify relation. (ii) If `n(A)=p` and R is reflexive defined on A then `Plen(R)leP^(2)`.

Discussion

38.	If the number of reflexive relations defined on a set A is 64, then the number of elements in A is _____A. 3B. 2C. 6D. 5
Answer» Correct Answer - A We have number of reflexive relations defined on A is `Z^(n-n)`, where n is the cardinal number of A. Given, `2^(n^(1)-n)=64rArr2^(n^(2)-n)=2^(6)` `rArr n^(2)-n=6rArr n(n-1)=3xx2` `therefore n=3`.

Discussion

39.	If `n(A)=40` and n(B)=23, then find n(A-B) and n(B-A) when `B sub A`.
Answer» Correct Answer - 17,0

Discussion

40.	In an election, two contestants A and B contested. X% of the total voters voted for A and (x+20)% for B. if 20% of the voters did not vote, then find x.A. 30B. 25C. 40D. 35
Answer» Correct Answer - A Apply the formula of `A cupB`

Discussion

41.	Which of the following statement(s) is/are true? (A) Every subset of an infinite set is infinite. (B) Every set has a proper subset. (C) Number of subsets of every set is even. (D) Every subset of a finite set is finiteA. A and BB. A,B and CC. B, C and DD. D
Answer» Correct Answer - D (a) Is false since the set N of all natural numbers is an infinite set having a finite subset, i.e., (1) (b) is false since `phi` has not proper subsets. (c) is false since number of subsets of an empty set is odd (i.e., `2^(@)=1`). (d) is clearly true.

Discussion

42.	For all p, such that `1leple100,n(A_(p))=p+1` and `A_(1)subA_(2)sub. . .. .subA_(100)`. Then `underset(p=1)overset(100)(U)A_(p)` contains. _______elementsA. 99B. 100C. 101D. 102
Answer» Correct Answer - C (i) Recall the definition of union of sets and subsets. (ii) If `AsubB`, then `A cupB=B`. (iii) `underset(n=1)overset(100)(U)A_(n)=A_(100)`. (iv) Now evalute `n(A_(100))` by using the given condition.

Discussion

43.	Every man in a group of 20 men likes either mangoes or an apple. Every man who likes apples also likes mangoes, 9 men like mangoes but not applies. How many like mangoes and apples?A. 9B. 11C. 10D. 12
Answer» Correct Answer - B Apply concept of subsets.

Discussion

44.	In a class, each student likes either cricket or football 40% of the students like football. 80% of the students like cricket. The number of studnets who like only cricket is 40 more than the number of students who like only football. What is the strength of the class?A. 80B. 100C. 120D. 150
Answer» Correct Answer - B (i) `n(FcupC)=n(F)+n(C)-n(FcapC)`. (ii) Let the total number of studetns be x. (iii) 80% of x-40% of x=40. find x.

Discussion

45.	X is the set of all engineering colleges in the state of A.P and R is a relation on X defined as two colleges are realted iff they are affiliated to the same university then R. isA. only reflexiveB. only symmetric.C. only transitive.D. equivalence.
Answer» Correct Answer - D (i) Verify the reflexvie, symmetric and transitive properties of relations. (ii) Take an example and proceed.

Discussion

46.	In a class, the number of students who like only Chess, only Caroms, both the games and neither of the games are in the ratio 2:4:1:3. the number of students who like at least one of these games is 120 more than those who like neither of the games. Find the number of studetns in the class.A. 300B. 240C. 270D. 360
Answer» Correct Answer - A Let the number of students who like only Chess be 2x. The number of students who like only Carroms. Both the games and neither of the gains are 4x,x and 3x respectively. Given, `2x+4x+x=3x+120` `rArr 4x=120rArrx=30` `therefore` The total number of students `=2x+4x+x+3x=10x=300`.

Discussion

Explore topic-wise InterviewSolutions in .

If `C subY` and `Y subX`, then_____

If `P=(1,2,3,4,5,6,7)` and `Q=(2,5,8,9)`, then find `P cup Q`.

Consider the following statements. `p:3 in(1,(3),5,7)` `q, 2 in(1,(3,4),4)` Which of the following is true?A. p aloneB. q aloneC. Both p and qD. Neither p nor q.

If A=(1,2,3), then the relation R={(1,1)(2,2),(3,1),(1,3)}` isA. reflexive.B. symmetricC. transitive.D. equivalence.

If `A={n:(n^(3)+5n^(2)+2)/(n)` is an integer and n itself is an integer}, then the number of elements in the set A isA. 1B. 2C. 3D. 4

If `A=(1,2,3)` and `B=(2,6,7)`, then `(A-B)cup(B-A)=`A. `phi`B. `mu`C. `(1,2,3,6,7)`D. `(1,3,6,7)`

Which of the following cannot be the cardinal number of the power set of any finite set?A. 26B. 32C. 8D. 16

If `n(A)=8` and `n(B)=6` and the sets A and B are disjoint, then find `n(AcupB)`.

The cardinal number of a set is 5. find the cardinal number of the power set.

A relation `R:Zrarr2` is such that `R={(x,y)//y=2x+1)` is aA. one to one relation.B. many to one relation.C. one to many relation.D. many to many relation.

If (x-y,x+y)=(2,8), then the values of x and y are respectively.A. 5,3B. 7,5C. 4,2D. 10,8

Let Z denote the set of integers, then `(x in Z,|x-3|lt4cap{x inZ:|x-4|lt5}`=A. {-1,0,1,2,3,4}B. {-1,0,1,2,3,4,5}C. {0,1,2,3,4,5,6}D. {-1,0,1,2,3,5,6,7,8,9}

If `n(P)=2` and `n(Q)=5000,` then `n(PxxQ)=`______

In `n(AcupB)=16` and `n(AcapB)=4`, then the number of elements in the symmetric difference of A and B is_____

If A=(1,2,3,4) then how many subsets of A contain the elements 3?A. 24B. 28C. 8D. 16

If `X=(x:x^(2)-12x+20=0)` and `Y=(x:x^(2)+5x-14=0)` , then X-Y=A. `(2)`B. `(10)`C. `(-7)`D. `()`

If `n(mu)=100,n(A)=50,n(B)=20` and `n(A cap B)`=10, then `n[(AcupB)]=`A. 60B. 30C. 40D. 20

If P and Q are disjoint, then P-Q=______ and Q-P=_________

The number of subsets of ` A xx B` if n(A)=3 and n(B)=3 isA. 512B. 256C. 511D. 235

If `P=(a,b,c,d)` and `Q=(1,2,3,4,5)` then `n(PxxQ)`=________

If `n(AxxB)` =45, then n(A) cannot beA. 15B. 17C. 5D. 9

If `P_(n)` is the set of first n prime numbers, then `underset(n=3)overset(10)capP_(n)` isA. {3,5,7,11,13,17,19}B. {2,3,5}C. {2,3,5,7,11,13,17}D. {3,5,7}

A relation `R,NrarrN` defined by `R={(x,y)//y=x^(2)+1)` isA. one to oneB. one to manyC. many to oneD. many to many.

If V=(a,e,i,o,u), then find the number of non empty proper subsets of V.

If `n(A)=6` and n(B)=3, then find the number of subsets of `A xx B`.

If `R={(a,b)//|a+b|=|a|+|b|}` is a relation on a set `{-1,0,1}` then R is_A. reflexiveB. symmetricC. anti symmetricD. equivalence.

If A={`p in N,p` is a prime and `p=(7n^(2)+3n+3)/(n)` for some `n in N`), then the number of elements in the set A isA. 1B. 2C. 3D. 4

If `R={(a,b)//|a+b|=a+b}` is a relation defined on a set (-1,0,1) then R is____A. reflexiveB. symmetricC. anti symmetricD. transitive.

The number of subsets of `{(a),(b,c),d,e)` is _____A. 32B. 16C. 8D. 20

A relation R: `ZrarrZ` defined by `R={(x,y)//y=x^(2)-1}` isA. one to one relation.B. many to one relation.C. many to many relationD. many to many relation.

Example of an equivalence relation among the following isA. is a father ofB. is less thanC. is congruent toD. is an uncle of

The relation is not equal to is defined on the set of real numbers is satisfies which of the following?A. Reflexive onlyB. Symmetric onlyC. Transitive onlyD. equivalence.

R and S are two sets such that n(R)=7 and R `cap` S`nephi` Further n(S)=6 and S `DeltaR`. The greatest. Possible value of `n(R DeltaS)` is____A. 11B. 12C. 13D. 10

If `R={(a,a),(a,c),(b,c),(b,b),(c,c),(a,b)}` on the set `X=(a,b,c)`, then how many subsets of R are reflexive relations?A. 15B. 16C. 8D. 9

Consider the following statements: (i) Every reflexive relation is anti-symmetric. (ii) Every symmetric relation is anti-symetric which among i and ii is true?A. i alone is trueB. ii alone is trueC. Both i and ii are trueD. Neither i nor ii is true.

If a set A has 13 elements and R is a reflexive relation on A with a elementss, ` n in Z^(+)`, thenA. `13lenle26`B. `0lenle26`C. `13lenle169`D. `0lenle169`

If the number of reflexive relations defined on a set A is 64, then the number of elements in A is _____A. 3B. 2C. 6D. 5

If `n(A)=40` and n(B)=23, then find n(A-B) and n(B-A) when `B sub A`.

In an election, two contestants A and B contested. X% of the total voters voted for A and (x+20)% for B. if 20% of the voters did not vote, then find x.A. 30B. 25C. 40D. 35

Which of the following statement(s) is/are true? (A) Every subset of an infinite set is infinite. (B) Every set has a proper subset. (C) Number of subsets of every set is even. (D) Every subset of a finite set is finiteA. A and BB. A,B and CC. B, C and DD. D

For all p, such that `1leple100,n(A_(p))=p+1` and `A_(1)subA_(2)sub. . .. .subA_(100)`. Then `underset(p=1)overset(100)(U)A_(p)` contains. _______elementsA. 99B. 100C. 101D. 102

Every man in a group of 20 men likes either mangoes or an apple. Every man who likes apples also likes mangoes, 9 men like mangoes but not applies. How many like mangoes and apples?A. 9B. 11C. 10D. 12

In a class, each student likes either cricket or football 40% of the students like football. 80% of the students like cricket. The number of studnets who like only cricket is 40 more than the number of students who like only football. What is the strength of the class?A. 80B. 100C. 120D. 150

X is the set of all engineering colleges in the state of A.P and R is a relation on X defined as two colleges are realted iff they are affiliated to the same university then R. isA. only reflexiveB. only symmetric.C. only transitive.D. equivalence.

If P and Q are disjoint, then P-Q= and Q-P=___