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QUESTION: 1

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

Solution:

Number of elements in a power set

2^{n}, where n = number of elements in the set P

hence, 2^{4}=16.

QUESTION: 2

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

Solution:

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.

QUESTION: 3

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

Solution:

**Correct Answer :- C**

**Explanation:- {2,4} wriiteen in set builder form is {x : 2 < x < 4}**

QUESTION: 4

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

Solution:

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.

QUESTION: 5

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

Solution:

The set containing all objects or elements and of which all other sets are subsets is Universal set

Here, option A have 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.

QUESTION: 6

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

Solution:

Clearly 0 is not an element of A ,so it must belong to A^{c}

So here 0 ∈ A^{c}

{0} ⊂ A^{c }w.r.t. X

QUESTION: 7

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

Solution:

First understand that a and b are fixed and x is movable. at any time x will be a and any time it will be b. basically x belongs to R and a and b are it's value at a time. Now come to the question [a, b] it means now there is a restriction on moving value of x here x will be start from a and ending with b.

QUESTION: 8

Which of the following statement is false?

Solution:

(a) True. {a,e} are two vowels of the English alphabet.

(b) True. Each element of {a} is also an element of {a,b,c}.

(c) True. {1,2,3} = {1,2,3}

However,Elements of first set is also the elements of seconds set.

(d) False. Each element of {a,b} is also an element of {b,c,a}.

QUESTION: 9

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

Solution:

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

QUESTION: 10

Choose the incorrect statement

Solution:

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

QUESTION: 11

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

Solution:

P contain {0, 1, 2, 3, 4} and Q contain natural no. which start with 1 and P= {0, 1, 2, 3, 4} Q ={1,2,3} here P isn't subset of Q because all the elements of P is not in Q

QUESTION: 12

Which of the following is a null set?

Solution:

|x| < 1 ⇒ -1 < x < 1

∴ No natural number exists between (-1, 1).

QUESTION: 13

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

Solution:

L.C.M of 4 and 6 is 12

QUESTION: 14

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

Solution:

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

QUESTION: 15

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

Solution:

**Number of proper subsets** of a given set = 2^{m }- 1, where m is the **number** of elements.

Here no. of elements are 3, So the no. of proper subets of A = 2^{3} - 1 =7.

QUESTION: 16

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

Solution:

As in the option c there are integers were as well as natural numbers. In another options there are only some of the elements of natural numbers.

QUESTION: 17

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

Solution:

2^{7 }= 128

QUESTION: 18

Choose the correct statement:

Solution:

{2} is a subset of {2, 4, 6}.

QUESTION: 19

Consider the set A of all divisors of 30. How many subsets of A contains even divisors only?

Solution:

Set of divisors of 30 = {1, 2, 3, 6, 10, 15, 30} in these the even divisors r = {2, 6, 10, 30} we know no.of subsets to any set = 2^{n} so answer is 2^{4 }= 16

QUESTION: 20

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

Solution:

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