CSCI 480, Math Exercises #1
• To make grading easier, please include the question with the answer. • Show your work and explain your answer. If the answer is an integer, I need to know how you got it.
1. Explicitly write out the contents of the following set: {X ∈P({1,2,3}) : 2 ∈ X}
2. Negate the following statement: If x is a rational number and x 6= 0, then tan(x) is not a rational number.
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.
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?
