1. Explicitly write out the contents of the following set: fX 2 P(f1; 2; 3g) : 2 2 Xg Answer: 2. Negate the following statement: If x is a rational number and x 6= 0, then tan(x) is not a rational number. Answer: 3. Compute how many 7-digit numbers can be made from the digits 1,2,3,4,5,6,7 if there is no repetition and the odd digits must appear in an unbroken sequence. Examples: 3571264 or 2415376 or 2467315, but not 7234615. Answer: 4. This problem concerns 4-card hands dealt off a standard 52-card deck. How many 4-card hands are there for which all 4 cards are of different suits or all 4 cards are red? Answer:
