Q17 of 71 Page 14

Find the number of subsets and the number of proper subsets of the following sets.

i. A = {13, 14, 15, 16, 17, 18}


ii. B = {a, b, c, d, e, f, g}


iii.

Number of subsets can be same as number of elements in its power set which is nothing but 2n elements. But for proper subset, there should be no element in the power set which is equal to our set itself, therefore 2n -1 elements.


i. number of subsets=26 =64,


number of proper subsets=26 -1= 63


ii. number of subsets=27 =128,


number of proper subsets=27 -1= 127


iii. number of subsets=21 =2,


number of proper subsets=21 -1= 1


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15

Examine whether A = {x : x is a positive integer divisible by 3} is a subset of B = {x : x is a multiple of 5, }

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Write down the power sets of the following sets.

i. A = {x, y}


ii. X = {a, b, c}


iii. A = {5, 6, 7, 8}


iv. A = Φ

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i. If A = Φ, find n[P(A)]

ii. If n(A) = 3, find n[P(A)]


iii. If n[P(A)] = 512 find n(A)


iv. If n[P(A)] = 1024 find n(A)

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If n[P(A)] = 1, what can you say about the set A?