Name:__________________________________
Math 201 – Fall 2023
Quiz 2
1. (12 points) Write the converse, the contrapositive, and the negation of the following
conditional, then determine whether the converse and contrapositive are true or false.
If either one is false, provide a counterexample.
Statement: If 𝑛 is divisible by 3, then 𝑛 is divisible by 6.
Converse:
Contrapositive:
Negation:
2. (8 points) Use a truth table to prove 𝑃 → 𝑄 ≡∼ 𝑃 ∨ 𝑄.
3. (10 points) Using only your result from #2 and the following rules, prove that
(𝑃 ∧ 𝑄) → 𝑅 ≡ 𝑃 → (∼ 𝑄 ∨ 𝑅).
De Morgan: ∼ (𝑃 ∧ 𝑄) ≡∼ 𝑃 ∨∼ 𝑄
Associative: (𝑃 ∨ 𝑄) ∨ 𝑅 ≡ 𝑃 ∨ (𝑄 ∨ 𝑅)