Find a counterexample to show that the following statements are false.

a): ?a, b ? R, ? a + b = ? a + ? b

b): ?a, b ? R, ? ab = ? a ? b

In this exercise the predicate P(x, y) denotes x + y = 1. What is the truth values of the following statements where x and y are integers.

a): ?x?y P(x, y)

b): ?x?y P(x, y)

c): ?x?yP(x, y)