Number of proper subsets of ${1, 2, 3, 4, 5, 6}$ is

64

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6

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63

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62

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Solution

The correct option is D $63$
Total number of elements in the given set is $n = 6$
Then, the total number of subset is $2^{n} = 2^{6} = 64$ and the number of proper subset is $2^{n} - 1$
So, the number of proper subsets is $64 - 1 = 63$

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If a set has 63 proper subsets, then it contains___ elements.

(A, B)

S = {1, 2, 3, 4, 5, 6}

A \cap B = ϕ

A \cup B = S

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