Question

Translate the following argument into symbolic form and determine wheter it's logically correct by constructing a truth table.

If the team wins, then the team remains in the playoffs. If the team stays in the playoffs, then the championship is within reach. Therefore, if the team wins, the championship is within reach.

Answer 1

let t = team wins

let r = team remains in playoffs

let c be championship within reach

let } = If x then y (The if, then part)

let :; = therefore

Thus,

t } r
r } c
:;t } c

This is a pure hypothetical statement.

FYI in the argument t } r, t is the antecedent and r is the consequent.

thus the argument is valid.