conjecture & counterexamples

Question

I need to figure out if the conjecture is true or false and if false, provide a counterexample for these.

1. the sum of any two consecutive prime numbers is also prime.
2. the product of two even numbers is always divisible by 2.
3. the difference between two negative numbers is always negative
4. for any integer x, x^2-x will always produce an even value
5. for any two integer x and y, |x+y| = |x| + |y|
6. If LM= MP, the M must be the midpoint of LP
7. All birds can fly
8. The difference between consecutive perfect square numbers is always odd.
9. for any two integers a and b, (a+b)^2 = a^2 +b^2

Answer 1

c. -2 - (-10) = 8

e. |-2 + 3| = |-2| + |3|, 1 = 5

f. The points could be non-collinear

g. Kiwi, Emu, Ostrich

i. (a + b)² = a² + 2ab + b²

Answer 2

a. 5+7= 12

b-g. trivial

h. true

i. trivial