8. Use truth tables to determine which of the following arguments are valid:

a. p ⇒ q q ⇒ r

\ r

b. p ⇒ (q ˅ ~ q)

q q ⇒ r

~ q ⇒ ~ r

\ r

c. p ⇒ q

~ q

\ ~ p

d. p ⇒ q ~ p \ ~ q

e. p ≡ q p ⇒ (r ˅ s)
q \ r ˅ s

f. p ⇒ q r ⇒ ~ q ~ (~ p ˄ ~ r)
\ q ˅ ~ q g. p ˄ q p ⇒ r q ⇒ ~ r \ r ˅ ~r h. The price of oil will continue to rise.
If the price of oil continues to rise then the value of the dollar will fall.
If the value of the dollar falls then Americans will travel less.
If Americans travel less then airlines will lose money.