1. No category

Math 51/COEN 19 Midterm review problems:
1. Prove that if x3 is irrational, then x is irrational (page 135 #38)
2. Prove that if m, n are integers, and m+n are odd, then exactly one of m and n is odd.
3. Show that the following statements about the real number x are equivalent: (page 105 #32)
i. x is rational
ii. x/2 is rational
iii. 3x-1 is rational
4. Let A, B, and C be sets. Prove or disprove: (A-B)-C = A-(B-C)
5. Find a closed formula for the function f, defined recursively as follows:
f(1) = 1
f(n+1) = f(n) +2n+1 , n≥1
6. Show that the function f(x) = ex from the set of real numbers to the set of real numbers is not
invertible. Is it possible to change the sets the function acts upon in order to make it invertible?
7. Prove that f(x) = |x| : R+ -> R+ is a bijection
8. Find the power set of the following set: {φ, { φ}, a, b}
9. Page 154 #31
10. Section 2.4 #15, #17
Note that this list is not exhaustive; in particular, it doesn’t include material from before Quiz 1,
which is fair game for the quiz.