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The correct ANSWER is (C) A⊂B and B⊂A

The best explanation: If SET A is EQUAL to set B then every ELEMENT of set A is in set B i.e. A⊂B and every element of set B is in set A i.e. B⊂A. Hence A⊂B and B⊂A.

Correct choice is (C) Infinite set

To explain: NULL set, void set, or empty set is a set which contains no ELEMENTS. Infinite set is a set having infinite number of elements.

Right option is (c) finite set

To explain I would say: Set of letters of English alphabet has 26 elements so it is a finite set.

It is not a SINGLETON, EMPTY or INFINITE set. Empty set has no element, singleton set has one element, infinite set has infinite NUMBER of elements.

The correct answer is (a) True

The best explanation: A collection becomes a set when it is WELL DEFINED for EXAMPLE a collection of good football PLAYERS is not a set since the PHRASE “good football players” is vague and not defined.

The correct choice is (d) {1,2}

Easy explanation: X^2-3x+2=0

=>x^2-x-2x-2=0=>x(x-1)-2(x-1)=0

=>(x-1)(x-2)=0=>x=1,2

so, the SOLUTION set of equation x^2-3x+2=0 in roster form is {1,2}.

The correct choice is (c) The COLLECTION of talented ACTORS in Hollywood

Best explanation: The collection of actors is not a set as there is no SPECIFIC criterion to determine WHETHER an ACTOR is talented or not.

The correct choice is (a) {3, 4} ⊂ A

To EXPLAIN: Here A has ELEMENTS 1,2, {3,4} and 5. So, {3, 4} ∈ A and {{3, 4}} ⊂ A.{1, 2, 5} ⊂ A. {3, 4} is not SUBSET of A.

The correct ANSWER is (d) infinite

Explanation: The set is infinite if it has infinite number of elements. Set having ZERO elements is empty set, set having ONE element is singleton set, set having FINITE number of elements is finite set.

Right CHOICE is (c) Equal SETS have the same ELEMENTS

The best explanation: If two sets A and B are equal then they are equivalent as well because all elements of A are in B and all elements of B are in A which means a number of elements in both sets are same.

Correct CHOICE is (b) {x: x Ɇ A and x € B}

For explanation I would say: The DIFFERENCE of a SET A and B is denoted as A-B. A-B is a set of those ELEMENTS that are in the set A but not in the set B. Similarly, the difference of a set B and A is denoted as B-A. It is a set of those elements that are in the set B but not in the set A.

Correct option is (b) {}

To EXPLAIN: A set is REPRESENTED by {}.

Usually, but not NECESSARILY a set is denoted by a capital letter e.g. A, B…….V, W, X, Y, Z.

The elements are enclosed between { } denoted by small LETTERS a, b, ……., y, z.

Right choice is (c) {1,4,6}

To explain: COMPLEMENT of a set A is a set which contains elements of U which are not the elements of B. So, B’ = U – B = {1, 2, 3, 4, 5, 6} – {2,3,5} = {1,4,6}.

Correct choice is (d) { }

The EXPLANATION is: Since A lie COMPLETELY INSIDE B so, A is a subset of B. All ELEMENTS of A also belongs to B. Hence, there is no element that lie in A and not in B. Set is { }.

Correct ANSWER is (b) 16

To explain: POWER set of set X is set of all subsets of set X. Set with m ELEMENTS has 2^m subsets. So, NUMBER of elements in power set of set X is 2^4=16.

The CORRECT option is (d) Y⊂X and Y⊂Z and X⊂Z

For EXPLANATION: Null SET is the subset of EVERY set so Y⊂X and Y⊂Z.

Since set X is equal to set Z so, Z⊂X and X⊂Z.

Right answer is (c) {3,4,7} and {7,4,3}

The best explanation: TWO sets A and B are SAID to be equal if every element of SET A is in set B and vice-versa.

{3,4,7} and {7,4,3} are equal.

The correct option is (d) zero or more but not infinite

Easy EXPLANATION: A FINITE SET can have any number of ELEMENTS EXCEPT infinity i.e. a finite set can have zero or more number of elements but not infinite.

Correct answer is (c) {x: -∞ < x < ∞}

Easy explanation: All the numbers whether it is an integer or RATIONAL number or IRRATIONAL number is defined as REAL Number. The RANGE of the real number LIES between in the range (-∞, +∞).

The correct choice is (c) {7}

EXPLANATION: 210=2*3*5*7 => U = {2,3,5,7}.

Complement of a set A is a set which CONTAINS elements of U which are not the elements of A. So, A’=U-A={2,3,5,7} – {2,3,5} = {7}.

Correct OPTION is (a) A

For EXPLANATION I would say: Here, A={1,2,3}, B={2,3,4}, C={2,3,5}, D={1,3,5,7}

A∪B={1,2,3}∪{2,3,4} = {1,2,3,4} and C∪D={2,3,5}∪{1,3,5,7} = {1,2,3,5,7}

(A∪B) ∩ (C∪D) = {1,2,3,4} ∩ {1,2,3,5,7} = {1,2,3} = A.

The correct answer is (d) U-A

The 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.

The correct ANSWER is (a) A

To explain I would say: INTERSECTION SIGNIFIES COMMON elements between two sets hence A has the common elements between A and B since A is a subset of B.

The CORRECT choice is (a) True

The explanation: 2x+1=0 => X= -1/2 which is not a natural number so it is an empty SET. Empty set is also a finite set as finite set have ZERO or more number of elements but not infinite.

Right ANSWER is (a) {a, B, c, d} and {d, c, b, a}

To elaborate: {a, b, c, d} and {d, c, b, a} are equal sets.

{4,8,12,16} and {8,12,16,18} are not equal their elements are not matching.

{X : x is a multiple of 10} = {10,20,30,………} which is infinite set and not equal to {10,20,30}.

{x : x is an even number} = {2,4,6,………….} which is an infinite set and not equal to {2,4,6}.

Correct option is (c) c

The best explanation: INTERSECTION of two sets A and B is the region COMMON to both SET A and set B.

In the GIVEN Venn diagram, common region is c so, A∩B is region c.

Right ANSWER is (C) RATIONAL numbers

To elaborate: Since set of rational numbers is superset for set of INTEGERS so it can be a universal set for integers. Rest are subset of integers so they can not act as the universal set for set of integers.

Right choice is (d) {Ф, {2}, {4}, {2,4}}

EASIEST explanation: The subsets of a SET are null set the set itself and a combination of all of its ELEMENTS.

The correct answer is (c) union of SETS of SCALENE and isosceles triangles

Explanation: A is set of equilateral triangles i.e. triangles with all THREE sides EQUAL.

Therefore, A’ is set of triangles with at least one side different i.e. MAY be all sides different or two sides equal so, A’ is union of sets of scalene and isosceles triangles.

Correct ANSWER is (c) 2^n

The explanation: NUMBER of SUBSETS of a SET having r elements each is nCr. Hence, the total number of subsets is ^nC0 + ^nC1 + ^nC2 + ……+^nCn = 2^n.

Right answer is (c) SET of letters of English ALPHABET

Best explanation: Set of letters of English alphabet can be considered as UNIVERSAL set for {a, P} because ‘a’ is a vowel and ‘p’ is a consonant.

The correct answer is (c) {2,3,4}

To explain I would say: Elements that lie inside the BOUNDARY of B are 2, 3, 4 so SET B = {2, 3, 4}. Elements LYING outside boundary of B are not part of B.

The correct option is (b) (3, -2) ∪ (1, 1) ∪ (2, 3)

Easy explanation: f(x) = (x – 1)(x – 2)(x – 3)/(x^3 + 6x^2 + 11x+ 6)

After solving the CUBIC equation (x^3 + 6x^2 + 11x+ 6) we get (x+1)(x+2)(x+3)

Now, we can see that this implies f(x) = (x – 1)(x – 2)(x – 3)/(x + 1)(x + 2)(x + 3)

So, the critical points of x are, x = 1, 2, 3, -1, -2, -3

So, for f(x) < 0 ᵾ x €(3, -2) ∪ (1, 1) ∪ (2, 3).

Correct option is (b) Universal set

To explain I would SAY: Universal set is the set which is a SUPERSET of all BASIC sets of that type.

Power set is the set of all subsets of given set. EMPTY set is the set which does not contain any element. SINGLETON set is the set that contains one element.

The correct option is (a) Set of REAL numbers

Easy explanation: If X is SUBSET of Y then Y is called superset of X. Set of RATIONAL numbers is subset of set of real numbers so, set of real numbers is called superset of X.

Correct OPTION is (C) 9

Easiest explanation: The above SET can be represented as {T,R,I,G,O,N,M,E,Y}. So, the number of elements in the set is 9.

The correct choice is (b) b

The explanation: There are five VOWELS in English Alphabet a, e, i, o, u. So, set can be WRITTEN in roster form as {a, e, i, o, u}. ‘b’ does not BELONGS to given set.

The correct OPTION is (b) False

For explanation: Given, N(T)=200, n(C)=300, n(T∩C) = 250

We KNOW, n(T∩C) ≤ n(T) and n(T∩C) ≤ n(C)

But here n(T∩C) ≤ n(T) is not valid so, data given is incorrect.