Determine the truth value of the compound statement (~p V q) → (~q V r) when p is false, q is true, and r is false.

Answer 1

~P is true

q is true

~p v q is true

the hypothesis (or antecedent) is true

the conclusion (or consequent) is false

R is false and ~q is false

the conditional says if true then false

so the conditional is false

hypothesis conclusion truth value

T T T

F F T

F T T

T F F

the only time a conditional is false is when the hypothesis is true and the conclusion is false

If A then B

means or is equivalent to

~A v B

Either B is true or A is false

that makes if A is true then B is false as a false statement.