1. Utilize definition of odd and even integers to prove that if x is odd integer and y is even integer, then 9x+5y-20 is an odd integer.
2. Utilize definition of rational numbers to prove that if u and v are rational then 8u+(3/2)v is rational.
3. Utilize definition of divisibility to prove given statement:
Consider a; b; c = Z with a != 0. If a\b and a\c then a\(6a + 5b - 3c).
4. Utilize definition of congruences to prove given statement:
Consider n = N and a; b; c; d = Z. If a =b (mod n) and c = d (mod n) then 2a - 7c = 2b - 7d (mod n).