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# Test: Algebra Of Sets

## 15 Questions MCQ Test Mathematics (Maths) Class 11 | Test: Algebra Of Sets

Description
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. The solved questions answers in this Test: Algebra Of Sets quiz give you a good mix of easy questions and tough questions. JEE students definitely take this Test: Algebra Of Sets exercise for a better result in the exam. You can find other Test: Algebra Of Sets extra questions, long questions & short questions for JEE on EduRev as well by searching above.
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:

∩ = {4}, ∴∪ (∩ C) = {1, 2, 3, 4}.

QUESTION: 3

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

Solution:

No. of proper subsets = 2n-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) = 23 = 8

∴ No. of elements in P(P(S)) = 28 = 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 = 2n, n ≤ 6, n ∈ N} and B = {x : x = 4n, n ≤ 2, n ∈ N}, then A – B is

Solution:

A = {x : x = 2n, n ≤ 6}
For (n = 1,2,3,4,5,6) {2,4,8,16,32,64}
B = {x : x = 4n, n ≤ 2}
For (n = 1,2) {4,8}
A - B = {2, 8, 32, 64}

QUESTION: 15

The set A = { x  :xRx2 = 16 and 2= 6 }

Solution:

x2 = 16 ⇒ x = ±4 and 2= 6 ⇒x = 3

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