Question

Let S = 0,1,5,4,7). Then the total number of subsets of Sis
(a) 64
(b) 32
(c) 40
(d) 20​

Answer 1

Number of subsets of set S are 32.

Option (b) is correct.

Given:

• A finite set.
• S={0,1,5,4,7}

To find:

• Find total numbers of subsets of S.
• (a) 64
• (b) 32
• (c) 40
• (d) 20

Solution:

Concept to be used:

• If a set have cardinal number n.
• Number of subsets of set are ${2}^{ n}$

Step 1:

Find the cardinal number of the set.

We know that cardinal number of set is nothing but total number of elements present in the set.

As there are 5 elements in the set S.

It is represented as n(S)= 5

Step 2:

Find number of subsets of S.

Total number of subsets of S$= {2}^{5}$

Total number of subsets of S=32

Thus,

Total number of subsets of S= 32

Option (b) is correct.

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Answer 2

Concept Introduction:-

It may be in the form of a word, a symbol, or a figure that reflects the arithmetic value of a quantity.

Given Information:-

We have been given that $S = (0,1,5,4,7)$.

To Find:-

We have to find that the total number of subsets of S.

Solution:-

According to the problem

Number of subset

$=2^n\\n=5$

Number of subsets

$=2^5\\=32$

Final Answer:-

The correct option is $(b)32$.

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