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Test: Subsets & Supersets - Commerce MCQ


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20 Questions MCQ Test Mathematics (Maths) Class 11 - Test: Subsets & Supersets

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

Let X= {1,2,3}, Y= {}, Z= {1,2,3}, then which of the following is true?

Detailed Solution for Test: Subsets & Supersets - Question 1

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.

Test: Subsets & Supersets - Question 2

If set A is equal to set B then ______.

Detailed Solution for Test: Subsets & Supersets - Question 2

Test: Subsets & Supersets - Question 3

Let X be set of rational numbers. Which of the following is not subset of X?

Detailed Solution for Test: Subsets & Supersets - Question 3

Set of rational numbers { x: x=p/q where p and q are integers and q≠0}.
Set of real numbers is not a subset of X. Set of natural numbers, whole numbers, integers are subset of X.

Test: Subsets & Supersets - Question 4

If P = {1, 2, 3, 4}, then the number of elements in its power set will be:

Detailed Solution for Test: Subsets & Supersets - Question 4

Number of elements in a power set = 2n, where n = number of elements in the set P.
Hence, 2= 16.

Test: Subsets & Supersets - Question 5

If E = {a, b, c, d, e} and A = {a, b, c} then A is:

Detailed Solution for Test: Subsets & Supersets - Question 5
  • A subset is a set whose elements are all members of another set.
  • Since all the elements of set A are the members of set E. So A is a subset of E.  
Test: Subsets & Supersets - Question 6

The interval (2, 4) written in set builder form is:

Detailed Solution for Test: Subsets & Supersets - Question 6

(2,4) written in set builder form is:
{x : 2 < x < 4}

Test: Subsets & Supersets - Question 7

How many elements does P(A) have, If A = Φ?

Detailed Solution for Test: Subsets & Supersets - Question 7

If A = Ф that means A does not contain any element i.e., n = 0.
Now, number of elements in a power set is 2n.
∴, n[P(A)] = 2⁰ = 1
Therefore P(A) contains 1 element.

Test: Subsets & Supersets - Question 8

Given the sets P = {2, 4, 6}, Q = {3, 5, 7} and R = {1, 3, 5, 7, 9}, which of the following may be considered as universal set for all the three sets P, Q and R?

Detailed Solution for Test: Subsets & Supersets - Question 8
  • The set containing all objects or elements and of which all other sets are subsets is a Universal set.
  • Here, option A has all the elements of set P, Q and R. So {1, 2, 3, 4, 5, 6, 7, 9} may be considered as universal set for all the three sets P, Q and R.
Test: Subsets & Supersets - Question 9

Let a, b ∈ R and a < b, then [a, b] implies:

Detailed Solution for Test: Subsets & Supersets - Question 9

Square brackets [a, b] implies that values of a and b should be included in the range of x i.e., a ≤ x ≤ b.

Test: Subsets & Supersets - Question 10

Let A = {2, 3, 4} and X = {0, 1, 2, 3, 4}, then which of the following statement is correct?

Detailed Solution for Test: Subsets & Supersets - Question 10
  • We have, Ac in X = The set of elements in X which are not in A = 0,1
  • {0} ∈ Ac w.r.t. X is false, because {0} is not an element of Ac in X.
  • ϕ ∈ Ac in X is false because ϕ is not an element of Ac in X.
  • {0} ⊂ Ac in X is correct because the only element of {0} namely 0 also belong to Ac in X.
  • 0 ⊂ Ac in X is false because 0 is not a set.
Test: Subsets & Supersets - Question 11

If A = {1, 3, 4} and B = {1, 4, 3, 2} then which of the following is true?

Detailed Solution for Test: Subsets & Supersets - Question 11

All the elements in set-A are presented in set-B. So "A" is a subset of "B".

Test: Subsets & Supersets - Question 12

Choose the incorrect statement:

Detailed Solution for Test: Subsets & Supersets - Question 12
  • A set A is a proper subset of a set B if A is a subset of B and there is at least one element of B that's not an element of A.
  • Thus, the void set is a subset of all sets, and it's a proper subset of every set except itself.
Test: Subsets & Supersets - Question 13

In which of the following statements, set P is not a subset of Q:

Detailed Solution for Test: Subsets & Supersets - Question 13
  • P contains {0, 1, 2, 3, 4} and Q contain natural numbers which start with 1 and P = {0, 1, 2, 3, 4} Q = {1, 2, 3}
  • Here P isn't a subset of Q because all the elements of P are not in Q.
Test: Subsets & Supersets - Question 14

Which of the following is a null set?

Detailed Solution for Test: Subsets & Supersets - Question 14

|x| < 1 ⇒ -1 < x < 1
∴ No natural number exists between (-1, 1).

Test: Subsets & Supersets - Question 15

If A = {x : x is a muliple of 4} and B = {x : x is a muliple of 6}, then A ∩ B consists of all multiples of:

Detailed Solution for Test: Subsets & Supersets - Question 15

L.C.M of 4 and 6 is 12.

Given, A = {x:x is a multiple of 4}
              = {4,8,12,16,20,…}


and     B = {x:x is a multiple of 6}
              = {6,12,18,24,…}


∴A ∩ B = {12,24,…}
             = {x:x is amultiple of 12}

Test: Subsets & Supersets - Question 16

A is a set with 6 elements. So, the number of subsets is:

Detailed Solution for Test: Subsets & Supersets - Question 16

{1, 2, 3, 4, 5, 6} is a set of 6 elements, so it has 26 = 64 subsets

Test: Subsets & Supersets - Question 17

If A = {a, b, c} then the number of proper subsets of A are:

Detailed Solution for Test: Subsets & Supersets - Question 17
  • Number of proper subsets of a given set = 2m - 1, where m is the number of elements.
  • Here the number of elements is 3. So the number of proper subsets of A = 23 - 1 = 7.
Test: Subsets & Supersets - Question 18

For the set of all natural numbers the universal set can be ______.

Detailed Solution for Test: Subsets & Supersets - Question 18

Integers contain all the natural numbers. So it can be a universal set for natural numbers. In other options, there are only some of the elements of natural numbers.

Test: Subsets & Supersets - Question 19

A set has 7 elements. The number of elements in its power set is:

Detailed Solution for Test: Subsets & Supersets - Question 19

Number of elements in power set = 2= 128

Test: Subsets & Supersets - Question 20

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect?

Detailed Solution for Test: Subsets & Supersets - Question 20

Here, A = {1, 2, (3, 4}, 5}

  • 1 is an element of the set. Hence 1 ∈ A is a correct statement.
  • In this set {3, 4} is treated as a single element of set A. That means {3,4} belongs to the set. Hence the statement given in option C, {3, 4} ∈ A is correct. 
  • 3, 4 are not the separate elements of set A. So {{3, 4}} ⊂ A is correct and {3, 4} ⊂ A is the wrong representation.

Hence the correct option is option A.

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