Answer
The argument is valid and utilises the Proof by division into cases
Work Step by Step
Let p, q and r be the statements:
p: I get a Christmas bonus.
q: I sell my motorcycle
r: I’ll buy a stereo
If I get a Christmas bonus, I’ll buy a stereo. (p → r)
If I sell my motorcycle, I’ll buy a stereo. (q → r)
∴ If I get a Christmas bonus or I sell my motorcycle, then
I’ll buy a stereo. (p ∨ q → r)
The argument follows the style of Proof by division into cases and hence is true.
p → r
q → r
p ∨ q
∴ r
