Question

Thus, A + (B + C) = (A + B) + C.

If D is a set, then the power set of D is the set PD of all the subsets of D. That is,

PD = {A: A ⊆ D}

The operation + is to be regarded as an operation on PD.

1 Prove that there is an identity element with respect to the operation +, which is _________.

2 Prove every subset A of D has an inverse with respect to +, which is _________. Thus, 〈PD, +〉 is a

group!

3 Let D be the three-element set D = {a, b, c}. List the elements of PD. (For example, one element is {a},

another is {a, b}, and so on. Do not forget the empty set and the whole set D.) Then write the operation

table for 〈PD, +〉.

Answer 1