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Right OPTION is (a) The SET of dogs with six legs

The best I can explain: CLEARLY there is no dog in this world with 6 legs hence this MAKES an empty set.

Correct OPTION is (b) False

For explanation: Since every PRIME number is not odd as 2 is EVEN prime number so set of prime numbers can not be considered as universal set for a set of odd numbers.

Correct choice is (d) {1,2,3,4,5,6,7,8,9,10}

For EXPLANATION: In {1,2,3,4,5,6,7,8,9,10}, 10 is not present in set U. So, it is not the subset of universal set. Rest all are SUBSETS of set U as their ELEMENTS are present in universal set.

The correct answer is (C) B∩A=A

To ELABORATE: An empty set is a subset of every set, also the union of a set with an empty set gives the set itself, SINCE, there are no elements in an empty set hence INTERSECTION with an empty set gives empty set.

The CORRECT answer is (b) (-∞, 1) ∪ (3, ∞) ∪ {2}

The explanation is: 1/(x – 1)(3 – x) ≤ 1

Now, on solving the equation further we get,

 1/(x – 1)(3 – x) -1 ≤ 0

This ALSO implies,

1- 1/(x – 1)(3 – x) ≥ 0

(x – 1)(3 – x) – 1/(x – 1)(3 – x) ≥ 0

So, (x – 2)^2/(x – 1)(3 – x) ≥ 0.

This implies, (-∞, 1) ∪ (3, ∞) ∪ {2}.

The correct OPTION is (b) 3

To ELABORATE: We know, n (T ∪ C) = n (T) + n (C) – n (T ∩ C)

Given, n (T ∪ C) = 7, n(T)=4, n(C)=5

7=4+5- n (T ∩ C)

n (T ∩ C) = 2.

n (only C) = n (C ∩ T’) = n (C) – n (T ∩ C) = 5-2=3.

3 members like only coffee.

The correct CHOICE is (d) {5,6}

For EXPLANATION I WOULD say: B-A is the set of ELEMENTS that BELONGS to B but not to A. Here, 5 and 6 belongs to B but not to A. So,

A = {1,2,3,4}

B = {3,4,5,6}

B-A = {3,4,5,6} – {1,2,3,4} = {5,6}.

Right option is (b) 20

The best I can explain: GIVEN, a + b + c + d = 100, a + c = 40, b + c = 30, c = 10

b+10=30 => b=20 i.e. 20 PERSONS LIKE only coffee.

Correct choice is (d) {2,3,4}

Explanation: Union of TWO SETS A and B is the region that INCLUDES entire set A and set B.

In the given VENN DIAGRAM, A∪B={2,3,4}.

The correct answer is (d) 60

Best explanation: We KNOW, n (F∪S) = n (F) + n (S) – n(F∩S)

GIVEN, n (F)=50, n (S)=20, n (F∩S) = 10

n (F∪S) = 50 + 20 – 10 = 60.

60 people speak at least one of the TWO LANGUAGES.

Correct choice is (a) {1,5}

To EXPLAIN: Elements that lie INSIDE the BOUNDARY of U but outside the boundary of A and B are 1,5. So, elements that belong to neither A nor B are 1,5. Set is {1,5}.

Right CHOICE is (B) equal sets

Easiest explanation: A-B is the SET of elements that belongs to A but not to B and B-A is the set of elements that belongs to B but not to A. A-B=B-A is POSSIBLE only when A and B are equal sets.

Correct CHOICE is (d) {3}

Easiest EXPLANATION: Element that lie INSIDE the boundary of B but OUTSIDE the boundary of A is 3. So, element that belongs to B but not A is 3. Set is {3}.

The correct CHOICE is (b) {2,4}

Explanation: Elements that LIE inside the boundary of A are 2 and 4 so SET A = {2,4}. Elements LYING outside boundary of A are not PART of A.

Right choice is (B) “A” and “B” are equal

To elaborate: The ROOTS of the equation x^2-3x+2=0 are 1 and 2 also A has the same elements, therefore, A and B are equal and equivalent as well as they have the same NUMBER of elements.

The correct CHOICE is (b) “A” and “B” are EQUIVALENT sets

To ELABORATE: Two sets are equal if each element in A is in B and vice versa. If a number of ELEMENTS in both sets are the same then they are equivalent sets.

The CORRECT ANSWER is (a) A is SUBSET of B

Easy explanation: In the given Venn diagram, A is completely INSIDE B which is completely inside U. So, A is subset of B and both A and B are subset of U.

Correct option is (B) {4,7,9}

To elaborate: {4,7,9} is finite set because it contains finite (countable) number of elements. Rest all are infinite SETS. {1,2,3,4,…………..} is a set of NATURAL numbers. {1,4,9,……………} is a set of SQUARE of natural numbers. {1,8,27,………………………} is a set of cube of natural numbers.

The correct choice is (C) {P,R,I,N,C,I,P,A,L}

To explain: A set has all unique ELEMENTS. So the set which contain all the elements of WORD PRINCIPAL and no letter is repeated. Hence, {P,R,I,N,C,I,P,A,L} cannot be a set.

Correct OPTION is (C) A∪A’

The BEST explanation: In the Venn DIAGRAM, A∩U=> region common to A and U is a i.e. A

A∩Φ’ = A∩U = A (Φ’=U)

A∪A’=>region a and region b => U

A∪Φ=A.

The CORRECT answer is (a) True

Explanation: Complement of a set A is a set that CONTAINS elements of U which are not the elements of A. So, A’=U-A= U∩A’.

(A’)’ = (U∩A’)’ = U’∪A = A.

Right choice is (b) False

To explain: For SET A to be the subset of B, whole set A must LIE inside set B which is not so in given Venn DIAGRAM so, set A is not subset of set B.

Correct answer is (a) True

The BEST EXPLANATION: SINCE set {a, b, e, i, o, u, v, z} has all the VOWELS so it can be CONSIDERED as the universal set for set of vowels.

Correct option is (d) B⊂C and A⊂C

The BEST I can EXPLAIN: Here A has two elements 1 and 3. They both belongs to C so, A⊂C.Here B has three elements 1, 5 and 9. They all belongs to C so, B⊂C.

Right answer is (a) True

Explanation: A quadratic EQUATION can have MAXIMUM two roots. So, the SET can have 0 to 2 NUMBER of elements so it must be a finite set.

Right choice is (b) Set of points on a line

For explanation I would say: There are infinite number of points on a line. So, the set of points on a line is infinite. REST all sets contain FINITE number of ELEMENTS.

Set of days of week has 7 elements and set of months in a year has 12 elements.Set of prime number less than 99 {2,3,5,7,11,……….,97}.

The correct CHOICE is (d) No point

The BEST explanation: Since parallel LINES do not INTERSECT anywhere they do not have any point in common. So, no point is common to parallel lines.

Right answer is (a) A collection of well-defined objects or element

Explanation: Generally, a set is defined as a collection of well defined objects or elements.

Each element in a set is unique.

Say for EXAMPLE, if S a set it is represented as,

S = {x: 2x^2ᵾ x< 5 and x € N}

Then the elements PRESENT in the set will be

S = {2, 8, 18, 32}.

The CORRECT answer is (C) ∈

To explain I WOULD say: Here, 2 is an element of SET A.

So, 2 belong to set A. 2∈A.

Right answer is (c) 300

To EXPLAIN: Since all people read newspaper so, N (T ∪ H) = 1000.

n(H) = 600 and n(T) = 700.

n (T ∪ H) = n (T) + n (H) – n (T ∩ H)

1000 = 700 + 600 – n (T ∩ H)

n (T ∩ H) = 1300-1000 = 300.

n (T’ ∩ H) = n(H)- n (T ∩ H) = 600-300 = 300.

300 persons read only Hindustan TIMES.

The correct choice is (b) 300

Best explanation: Since all PEOPLE read NEWSPAPER so, n (T ∪ H) = 1000.

n(H) = 600 and n(T) = 700.

n (T ∪ H) = n (T) + n (H) – n (T ∩ H)

1000 = 700 + 600 – n (T ∩ H)

n (T ∩ H) = 1300-1000 = 300.

Correct CHOICE is (C) {1,2,3,4,5,6}

For explanation: UNION of SET A and B is a set that contains all the elements of set A and set B.

A = {1,2,3}

B = {3,4,5,6}

A∪B = {1,2,3,4,5,6}.

Correct option is (B) B⊆A

The explanation: B is {1,2,3…….} and A is {0,1,2,3….} clearly both are INFINITE SETS and A has 1 extra element 0 so B is a subset of A.

Correct option is (c) 30

The explanation: Given, a + b + c + d = 100, a + c = 40, b + c = 30, c = 10

a+10=40 => a=30 i.e. 30 persons LIKE only TEA.

Right ANSWER is (B) B is a SUBSET of A

To explain: All elements of B belong to A, so B is a subset of A and A is a SUPERSET of A.

Right choice is (d) may or may not

Explanation: A FINITE SET can have ZERO or more NUMBER of ELEMENTS but not infinite so, finite set may or may not be empty set. Empty set is a set with no element in it.