math

posted by viola

1) find the power set of 446
2) find the power of (c,d,e,f,y )
3)if X=(2,4,6,8 )
Y=(3,6,9)
Z=( 1,3,6,8)

1. MathMate

(a) a power set of a set A is a set of all possible subsets of A. Assuming 446 is a single element, or A={446}, then the power set consists of ∅, and {446}. In general, if A has n elements, the cardinality of the power set of A is 2^n, or has 2^n elements.

(b) the power set of {c,d,e,f,y} has 2^5=32 elements, including ∅.
there are
1 set with no elements: ∅
5 sets with one elements:{c},{d}...
10 sets with two elements:{c,d},{c,e},...
10 sets with three elements: {c,d,e}...
5 sets with four elements: {c,d,e,f},...
1 set with 5 elements.
Total=32 sets.

(c) not sure if question is complete.

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