1- By using the truth tables, show that: $(p \lor q) \land (\neg p \lor r) \to (q \lor r) = T$
2- By using the direct proof to show that:
If a, b and c are integers, a + b is even, and b + c is even, then a + c is even.
3- Use the mathematical induction to prove that for all natural numbers n,
$-1 + 2 - 3 + 4 + \dots + (2n - 1) + 2n = n$
4- Use the proof by contradiction to show that:
$\sqrt{5} + \sqrt{7} + \sqrt{11} < \sqrt{71}$
5- Use the proof by cases to prove that the expression $2n^2 + n - 5$ is not divisible by 3 for all
integer n. (Hint: when integer is divided by 3, then the possible reminders are 0, 1 or 2. So
study 3 cases: n = 3a, n = 3a + 1, n = 3a + 2 for integer a)
