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This contains 25 Multiple Choice Questions for JEE Test: Sets 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If n (A) = 3 and n (B) = 6 and A ⊆ B, then the number of elements in A ∪ B is equal to

Solution:

n(A) = 3, n(B) = 6

It is given that A is a subset of B which means that all elements of A are present in B.

n(A∪B) = n(A) + n(B) - n(A∩B) ----------- [ As A⊂B ]

= 3 + 6 - 3 = 6

QUESTION: 2

If n (A) = 3 and n (B) = 6 and A ⊆ B, then the number of elements in A ∩ B is equal to

Solution:

Since n(A) = 3 n(B) = 6

A⊆B,A⊂B=B

So, n (A⋂B) =n(A) =3

QUESTION: 3

Let A and B be subsets of a set X, Then which of the following is correct

Solution:

A - B means part of A that does not contain B,

So, A - B = A−(A∩B)

= A ∩ B^{c}

QUESTION: 4

If A , B and C are any three sets, then A – (B ∪ C) is equal to

Solution:

According to De'Morgan's Law;

A-(BUC) = (A-B)∩(A-C)

QUESTION: 5

What is the cardinality of the set of odd positive integers less than 10?

Solution:

Set S of odd positive an odd integer less than 10 is {1, 3, 5, 7, 9}. Then, Cardinality of set S = |S| which is 5.

QUESTION: 6

If A, B and C are any three sets, then A ∩ (B ∪ C) is equal to

Solution:

In the problem statement we are taking union of B and C and then taking its intersection with A.

This means A∩(B∪C)will contain elements that are in A and are in either B or C.

∴ A∩(B∪C) is equivalent to taking intersection of A,B and A,C and then taking there union i.e. (A∩B)∪(A∩C)

QUESTION: 7

If aN = {ax : x ∈ N}, then the set 3N ∩ 7N is

Solution:

According to the given notation,

3N = {3x:x∈R} = {3,6,9,12.......}

and 7N = {7x:x∈R} = {7,14,21,28,35,42,.......}

Hence 3N∩7N = {21,42,63}

= {21x:x∈N}

= 21N

QUESTION: 8

The smallest set A such that A ∪ {1, 2} = {1, 2, 3, 5, 9} is

Solution:

Let A be the smallest set.

A ∪ {1,2} = {1,2,3,5,9}

A = {3,5,9} or {1,2,3,5,9}

As A is smallest set,we take A = {3,5,9} only

Check:-

{3,5,9} ∪ {1,2} = {1,2,3,5,9}

QUESTION: 9

If A and B are sets, then A ∩ (B – A) is

Solution:

As we know that A-B = A

that implies x ∈ A ∩ B

⇒ x ∈ A and x ∈ B

⇒ x ∈ to A-B and x ∈ B

⇒ (x ∈ A and x doesnt belongs to B) and x ∈ to B

So, our assumption is wrong

⇒ A∩B = ϕ

QUESTION: 10

If A = {0,1,5, 4, 7}. Then the total number subsets of A are

Solution:

QUESTION: 11

If A and B be two sets such that n (A) = 70, n (B) = 60, and n (A ∪ B) = 110. Then n (A ∩ B) is equal to

Solution:

QUESTION: 12

Which set is the subset of all given sets?

Solution:

The question should be: “Which set is the subset of all the sets?”

Φ = { } (Empty set) is a subset of all the sets.

QUESTION: 13

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A U B

Solution:

We know that

n(A∪B)=n(A)+n(B)−n(A∩B)......(i)

n(A∪B)=n(A)+n(B)-n(A∩B)......(i)

Case 1 From (i) , it is clear that n(A∪B)

n(A∪B) will be maximum when n(A∩B)=0

In that case,

n(A∪B)=n(A)+n(B)=(3+6)=9

∴ Maximum number of elements in

(A∪B)=9

Case 2 From (i) , it is clear that n(A∪B)

n(A∪B) will be minimum when n(A∩B)=0 maximum ,i.e, when

n(A∩B)=3

In this case,

n(A∪B)=n(A)+n(B)−n(A∩B)=(3+6−3)=6

∴ minimum number of elements in

A∪B=6

QUESTION: 14

If A = {x : x ≠ x} represents

Solution:

QUESTION: 15

If A = {x : x^{2} − 5x + 6 = 0}, B = {2, 4}, C = {4, 5}, then A × (B ∩ C) is

Solution:

Clearly, A = {2, 3}, B = {2, 4}, C = {4,5} B ∩ C = {4}

∴ A × (B ∩ C) = {(2, 4), (3, 4)}.

QUESTION: 16

Which of the following is a set

Solution:

QUESTION: 17

Let A = {x : x ∈ R, |x| < 1}; B = {x : x ∈ R, |x − 1| ≥ 1} and A ∪ B = R − D, then the set D is (R ∈ Set of real numbers)

Solution:

A = {x : x ∈ R,−1 < x < 1}

B = {x : x ∈ R : x − 1 ≤ −1 or x − 1 ≥ 1]

= {x : x ∈ R : x ≤ 0 or x ≥ 2}

∴A ∪ B = R − D , where D = [x : x ∈ R,1 ≤ x < 2]

QUESTION: 18

If A, B and C are non-empty sets, then (A - B) U (B - A) equals

Solution:

Use venn diagram approach

QUESTION: 19

Which of the following statements is true?

Solution:

Since the curly brackets denote a set, so the other three options are a subset of the set {1, 2, 3} and and only 3 belongs to the set.

QUESTION: 20

If a set A has n elements, then the total number of subsets of A is

Solution:

QUESTION: 21

If A, B, C be any three sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C, then

Solution:

Given that AUB = AUC

⇒ (AUB) ∩ C = (AUC) ∩C

⇒ (A∩C) U (B∩C) = C [ ∴(AUC)∩C = C ]

⇒ (A∩B) U (B∩C) = C ..........(1) [ ∴ (A∩C) = A∩B ]

Again AUB = AUC

(AUB) ∩ B = (AUC) ∩ B

B = (A∩B) U (C∩B)

= (A∩B) U (B∩C) ...........(2)

From 1 & 2 we get

B = C

QUESTION: 22

Given the sets A = {1, 2, 3}, B = {3 , 4}, C = {4 , 5, 6}, then A ∪ (B ∩ C) is

Solution:

QUESTION: 23

If A = {a, b}, B = {c, d}, C = {d, e}, then {(a, c), (a, d),(a, e), (b, c), (b, d), (b, e)} is equal to

Solution:

QUESTION: 24

Two finite sets have m and n elements. The total number of subsets of the first set is 48 more than the total number of subsets of the second set. The values of m and n are

Solution:

Total number of subsets of the first set = 2^{m}

Total number of subsets of the second set = 2^{n}

2^{m} = 2^{n} + 48

By hit and trial,

m = 6, n = 4

QUESTION: 25

Let A = {x : x is a prime factor 240} and B = {x : x is the sum of any two prime factors of 240}. Then

Solution:

A = {2, 5, 3} and B = {7, 8, 5} and A ∪ B = {2, 3, 5, 7, 8}

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