Question

Consider the following argument:

If pigs have wings, then pigs can fly.

If pigs are lighter than air, then pigs can fly.

Pigs have wings or pigs are lighter than air.

If pigs have wings or pigs can fly, then pigs don’t have wings.

Therefore, donkeys can fly.

(a) Write this argument in symbolic form, using the variables listed below.

Pigs can fly p

Pigs are lighter than air q

Pigs have wings r

Donkeys can fly s

(b) Determine whether the argument is valid or not. Show your working.

Answer 1

`r \Rightarrow p\\ q \Rightarrow p\\ r \vee p\\ (r \vee q) \Rightarrow \\eg r\\ s`

Explanation:

`r \Rightarrow p \equiv (\\eg r \vee p)`, p is false.

`q \Rightarrow p \equiv (\\eg q \vee p)`, p is false.

`(r \vee q)`, r and q are falses.

`(r \vee q) \Rightarrow \\eg r \equiv (\\eg (r \vee q) \vee \\eg r)`. this sentence is true.

s