What is the cardinality of the set {ø, {ø}}?

a) ø 0

b) {ø} 1

c) {ø,{ø}} 2

d) {ø,{ø}, {ø,{ø}}} 3

#3. a) Section 1.6, page 85, #16: Can you conclude that A = B if A and B are 2 sets with the same power set? Why or why not?

The union of all the sets in the power set of X is X, so we can recover a set from its power set. The answer is "yes"

b) Section 1.6, page 86, #22: Suppose that A x B = ø, where A and B are sets. What can you conclude?

One of A or B (or both) must be empty (if neither A nor B were empty, there would be an element in AxB)

#4. a) Section 1.7, page 95, #14a, e: Let A, B and C be sets. Show that

a) (A U B) (A U B U C)

(i) in words by showing the appropriate subset relations as done in class

Suppose x A U B

Then x A or B

Therefore x A U B U C

(truthfully, this is almost given to be true by the definition of union)

b) (B - A) U (C - A) = (B U C) - A

We need to show:

1. (B - A) U (C - A) Í (B U C) - A

and 2. (B U C) - A Í (B - A) U (C - A)