Chapter 1 Test

p ≡ "You are in Seoul." q ≡ "You are in Kwangju." r ≡ "You are in South Korea." p → (r ∧ ¬q)

If you are in Seoul, then you are in South Korea, but you are not in Kwangju.

p ≡ "You are in Seoul." q ≡ "You are in Kwangju." r ≡ "You are in South Korea." ¬r → ¬(p ∨ q)

If you are not in South Korea, then you are not in Seoul or Kwangju.

S ≡ If you are studying hard, then you are staying up late at night. give the converse

If you are staying up late at night, then you are studying hard. p → q ≡ q → p

Let Q be a quadrilateral. Given the statements: If Q is a rhombus, then Q is a parallelogram. Q is not a parallelogram. what statement follows by modus tollens?

Q is not a rhombus.

Which derivation rule justifies the following argument? If n is a multiple of 4, then n is even. However, n is not even. Therefore, n is not a multiple of 4.

modus tollens