Logical Equivalencies

Question 1

p → q ≡

Answer 1

¬p ∨ q

¬q → ¬p

Question 2

p ∨ q ≡

Answer 2

¬p → q

Question 3

p ∧ q ≡

Answer 3

¬(p → ¬q)

Question 4

¬(p → q) ≡

Answer 4

q ∧ ¬q

Question 5

(p → q) ∧ (p → r) ≡

Answer 5

p → (q ∧ r)

Question 6

(p → r) ∧ (q → r) ≡

Answer 6

(p ∨ q) → r

Question 7

(p → q) ∨ (p → r) ≡

Answer 7

p → (q ∨ r)

Question 8

(p → r) ∨ (q → r) ≡

Answer 8

(p ∧ q) → r

Question 9

¬(p ∧ q) ≡

Answer 9

(¬p ∨ ¬q)

Question 10

NOT BICONDITIONAL

p only if q
is paraphrased
not p if not q
which is further paraphrased
if not q, then not p
which is symbolized as ... ?

What is this logically equivalent to?

Why is this problem?

Answer 10

¬q → ¬p

same as

p → q

problem because we are led to believe that

p only if q ≡ p → q