Question

1. If A = {(a, b) c}, find the power set P(A)

Answer 1

Step-by-step explanation:

P(A) = {0, {a}, {b}, {c}, {a,b}, {a,c}, {b,c} }

I know that the power set includes the empty set as well and that a power set has 2^n elements in the set. Therefore 2^3 = 8 elements in the set.

Answer 2

Answer:

$A[(a,b),c]=[$∅, $(a,b),(c),[(a,b),c]]$

Step-by-step explanation:

The power set, $P(A),$ of any set, $A,$ is the set of all subsets of the set including the empty set, ∅, and the set itself.

The given set has two elements, $A=(a,b),$ and $B=c,$ so its power set has $2^2=4$ elements, the four subsets:

     ∅,$(A),(B),(A,B)$

You can expand that to include all the braces, but try not to confuse yourself with the levels:

$A[(a,b),c]=[$∅, $(a,b),(c),[(a,b),c]]$