Use a contrapositive proof to prove the following argument O

Use a contrapositive proof to prove the following argument: Only a fool would lie about one of Elaine\'s sorority sisters to her. A classmate of Elaine\'s lied about Joanne to her. Therefore, if none of Elaine\'s classmates are fools, then Joanne is not a sorority sister of Elaine. (F(x) = x is a fool; L(x,y,z) = x lies about y to z ; C(x,y) = x is a classmate of y; S(x,y) = x is a sorority sister of y; e = Elaine ; j = Joanne)

Solution

We assume Joanne is a sorority sister of Elaine.

In other words, S(j,e) = Joanne is sorority sister, TRUE (Contrapsitive assumption)

C(x,e) = x is classmate of Elaine TRUE

L(x, j, e) = x lies to Elaine about Joanne TRUE

F(x) = x is a fool which if FALSE would lead to S(j, e) ! = j