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1. Can you conclude that A=B given that (please explain). Hint: another way to ask this question is: (in part a, if A∪C = B∪C is it true that A=B?).  If it’s true, provide a proof.  If it’s not give examples of A, B and C such that A∪C = B∪C is true, but A=B is false.

a. A∪C = B∪C ?

b. A∩C = B∩C ?

2. Use a Venn Diagram to show True or False:

A∆(B∩C) = (A∆B)∩(A∆C)

3. Let A, B, C be three sets such that:

A = {2,3,4}

B = {4,6,7}

C = {7,9,10}

Determine the following (write out the set):

(A∩B)∪C =

A∩(B∪C) =

4. How many permutations of the 26 letters of the alphabet contain the pattern “OUT” or the pattern “DIG”

5. In a 5-card poker hand, what is the probability of getting a full house (three of the same number, and also a pair of something else)?