Fsc Part 1 Mathematics (Complete Solution)

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Q8

What is the number of elements of the power set of each of the following sets?

**(i) { }**

Ans:Since the set { } has zero elements, so its power set will have 2^{0}=1 elements.

**(ii) {0,1}**

Ans:Since the set {0,1 } has two elements, so its power set will have 2^{2}=4 elements.

**(iii) {1,2,3,4,5,6,7}**

Ans:Since the set {1,2,3,4,5,6,7 } has seven elements, so its power set will have 2^{7}=128 elements.

**(iv) {0,1,2,3,4,5,6,7}**

Ans:Since the set {0,1,2,3,4,5,6,7 } has seven elements, so its power set will have 2^{8}=256 elements.

**(v) {a, {b,c} }**

Ans:Since the set {a,{b,c}} has two elements, so its power set will have 2^{2}=4 elements.

**(vi) { {a,b},{b,c,},{d,e} }**

Ans:Since the set **{ {a,b},{b,c,},{d,e} }** has three elements, so its power set will have 2^{3}=8elements.