Q16 of 71 Page 14

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

Power set is nothing but all the possible combinations of the available set. Which can form a subset of that power set. For a set with ‘n’ elements, we will have 2n elements in the power set.


i. P(A) = {Φ {x}, {y}, {x, y}} - 22 =4 elements


ii. P(X)= {Φ, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}} – 23 =8 elements


iii. P(A) = {Φ, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8}, {5, 6, 7, 8}} – 24 =16 elements


iv. P(A) = {Φ} – 20 =1=one element


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14

Let X = {−3, −2, −1, 0, 1, 2} and Y = {x : x is an integer and −3 ≤ x < 2}

i. Is X a subset of Y?


ii. Is Y a subset of X?

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

 17

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

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


iii.

18

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)