Test: Algebra Of Sets - Commerce MCQ

# Test: Algebra Of Sets - Commerce MCQ

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

Test: Algebra Of Sets for Commerce 2024 is part of Mathematics (Maths) Class 11 preparation. The Test: Algebra Of Sets questions and answers have been prepared according to the Commerce exam syllabus.The Test: Algebra Of Sets MCQs are made for Commerce 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Algebra Of Sets below.
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Test: Algebra Of Sets - Question 1

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

Detailed Solution for Test: Algebra Of Sets - Question 1

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

Test: Algebra Of Sets - Question 2

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

Detailed Solution for Test: Algebra Of Sets - Question 2

∩ = {4}, as only 4 is common between B and C
∪ (∩ C) = {1, 2, 3, 4}.

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Test: Algebra Of Sets - Question 3

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

Detailed Solution for Test: Algebra Of Sets - Question 3

No. of proper subsets = 2n-1

Test: Algebra Of Sets - 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)’?

Detailed Solution for Test: Algebra Of Sets - Question 4

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}

Test: Algebra Of Sets - Question 5

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

Detailed Solution for Test: Algebra Of Sets - Question 5

If A = {5, 10, 15}, B = ϕ
B - A will have those elements which are in B but not in A.
B - A = ϕ

Test: Algebra Of Sets - Question 6

A = Set of all triangles
B = Set of all right triangles
A – B = ?

Detailed Solution for Test: Algebra Of Sets - Question 6

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

Test: Algebra Of Sets - Question 7

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

Detailed Solution for Test: Algebra Of Sets - Question 7

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

Test: Algebra Of Sets - Question 8

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

Detailed Solution for Test: Algebra Of Sets - Question 8

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.

Test: Algebra Of Sets - Question 9

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

Detailed Solution for Test: Algebra Of Sets - Question 9

Test: Algebra Of Sets - Question 10

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

Detailed Solution for Test: Algebra Of Sets - Question 10

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}

Test: Algebra Of Sets - Question 11

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

Detailed Solution for Test: Algebra Of Sets - Question 11

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}

Test: Algebra Of Sets - Question 12

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

Detailed Solution for Test: Algebra Of Sets - Question 12

No. of elements in P(S) = 23 = 8

∴ No. of elements in P(P(S)) = 28 = 256

Test: Algebra Of Sets - Question 13

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

Detailed Solution for Test: Algebra Of Sets - Question 13

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.

Test: Algebra Of Sets - Question 14

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

Detailed Solution for Test: Algebra Of Sets - Question 14

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}

Test: Algebra Of Sets - Question 15

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

Detailed Solution for Test: Algebra Of Sets - Question 15

x2 = 16 ⇒ x = ±4 and 2= 6 ⇒x = 3

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

## Mathematics (Maths) Class 11

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## Mathematics (Maths) Class 11

75 videos|238 docs|91 tests