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This mock test of Test: Algebra Of Sets for JEE helps you for every JEE entrance exam.
This contains 15 Multiple Choice Questions for JEE Test: Algebra Of Sets (mcq) to study with solutions a complete question bank.
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QUESTION: 1

U = Set of all teachers in a school and B = Set of all Mathematics teachers in a school, So B’ =?

Solution:

U = Set of all teachers in a school

B = Set of all Mathematics teachers in a school

B’ = U – B = Set of all Non-Mathematics teachers in a school

QUESTION: 2

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

Solution:

*B *∩ *C *= {4}, ∴* A *∪ (*B *∩ *C*) = {1, 2, 3, 4}.

QUESTION: 3

The number of proper subsets of the set {1, 2, 3} is

Solution:

No. of proper subsets = 2^{n}-1

QUESTION: 4

If U = set of all whole numbers less than 12, A = set of all whole numbers less than 10, B = Set of all odd natural numbers less than 10, then what is (A ∩ B)’?

Solution:

U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

B = {1, 3, 5, 7, 9}

A ∩ B = {1, 3, 5, 7, 9}

(A ∩ B)’ = U - (A ∩ B)

(A ∩ B)’ = {0, 2, 4, 6, 8, 10, 11}

QUESTION: 5

If A = {5, 10, 15}, B = ϕ, then B – A is

Solution:

If A = {5, 10, 15}, B = ϕ

B - A will have those elements which are in B but not in A.

B - A = ϕ

QUESTION: 6

A = Set of all triangles

B = Set of all right triangles

A – B = ?

Solution:

A = Set of all triangles

B = Set of all right triangles

A – B = Set of triangles after removing all right triangles from A

= Set of all triangles which do not have right angle

QUESTION: 7

If A = {2, 4, 6, 8} and U = {1, 2, 3, 4, 5, 6, 7, 8, 9,}, then A’=

Solution:

U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {2, 4, 6, 8}

A’ = U – A

A’ = {1, 3, 5, 7, 9}

QUESTION: 8

The number of elements in the Power set P(S) of the set S = {{Φ}, 1, {2, 3}} is

Solution:

There’s a result in mathematics used for this. It says that a power set B of any set A is a set of all the subsets of A and the number of elements of B will be 2^n where n is the number of elements of A.

So taking your question as an example;

A = {1,2,3}

B : set of all subsets of A

List out all the subsets of A - {1},{2},{3},{1,2},{2,3},{1,3},{1,2,3},{empty set}

Number of elements in A (n) = 3

so 23 = 8

So, B = {{1},{2},{3},{1,2},{2,3},{1,3},{1,2,3},{empty set}}

and the number of elements are 8.

QUESTION: 9

A = {1, 2, 3, 4, 5} and B = {2, 3, 7} So A – B =?

Solution:

QUESTION: 10

If A = {1, 2, 3, 4} and B = {4, 5, 6, 7, 8}, then A U B = ?

Solution:

In set theory, if A and B are sets, then the union of A and B , written A ⋃ B, is {x: x ∈ A or x ∈ B}. By asserting that x ∈ A or x ∈ B, we do not exclude the possibility that x is a member of both A and B. Further, if the same object/element is member of both A and B, then that element is counted only once in the new set formed by the union of A and B.

Given, A = {1,2,3,4} and B = {4,5,6,7,8}.

∴ By definition, A ⋃ B = {1,2,3,4,5,6,7,8}

QUESTION: 11

If U = {1,2, 3, ….,10}, A = {2, 4, 6}, B = {3, 4, 6, 8, 10,}, then (A ∩ B)’ is

Solution:

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {2, 4, 6}

B = {3, 4, 6, 8, 10}

A ∩ B = {4, 6}

(A ∩ B)’ = U – (A ∩ B)

= {1, 2, 3, 5, 7, 8, 9, 10}

QUESTION: 12

A set S contains 3 elements, the number of subsets of which of the following sets is 256

Solution:

No. of elements in P(S) = 2^{3} = 8

∴ No. of elements in P(P(S)) = 2^{8} = 256

QUESTION: 13

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: 14

If A = {x : x = 2^{n}, n ≤ 6, n ∈ N} and B = {x : x = 4^{n}, n ≤ 2, n ∈ N}, then A – B is

Solution:

A = {x : x = 2^{n}, n ≤ 6}

For (n = 1,2,3,4,5,6) {2,4,8,16,32,64}

B = {x : x = 4^{n}, n ≤ 2}

For (n = 1,2) {4,8}

A - B = {2, 8, 32, 64}

QUESTION: 15

The set *A* = { *x *:*x* ∈ *R*, *x*^{2} = 16 and 2*x *= 6 }

Solution:

*x*^{2} = 16* ⇒ x *= ±4 and 2*x *= 6* ⇒x *= 3

There is no value of x which satisfies both the above equations. Thus, *A *= *φ*

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