Q18 of 71 Page 14

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)

As we have seen in the previous problems, the number of elements in the power set are 2n elements, while there are n elements in the current set. Similarly, if there are n elements in the power set, then there will be Log2(n) elements in the current set.


i. 20 =1


ii. 23 =8


iii. Log2(512)=9


iv. Log2(1024)=10


More from this chapter

All 71 →
16

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

 17

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.

19

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

 20

Let

A = {x : x is a natural number < 11}


B = {x : x is an even number and 1 < x < 21}


C = {x : x is an integer and 15 ≤ x ≤ 25}


i. List the element of A, B, C


ii. Find n(A), n(B), n(C)


iii. State whether the following are True (T) or False (F)


a)


b)


c)


d)