Question

How many subsets does the set D={c,a,t}D={c,a,t} have?

Answer 1

The number of all possible subsets of D is 8.

Explanation:

Consider the provided set D={c,a,t}

The subset of D contains no elements: { }

The subset of D contains one element each: {c} {a} {t}

The subset of D contains two elements each: {c, a} {a, t} {c, t}

The subset of D contains three elements: {c, a, t)

Hence, all possible subsets of D are { }, {c}, {a}, {t}, {c, a}, {a, t}, {c, t}, {c, a, t}

Therefore, number of all possible subsets of D is 8.

Or we can use the formula:

The number of subsets of the set is
`2^n` If the set contains ‘n’ elements.

There are 3 elements in the provided set, thus use the above formula as shown:

2³=8

Hence, the number of all possible subsets of D is 8.