I've attached the file need help for exams I'm preparing..
A Arweee New member Joined Apr 11, 2021 Messages 1 Apr 11, 2021 #1 I've attached the file need help for exams I'm preparing..
L lex Full Member Joined Mar 3, 2021 Messages 965 Apr 11, 2021 #2 (A) [MATH]\exists x(F(x) \land S(x)) \rightarrow (y)(M(y) \rightarrow W(y))[/MATH](B) [MATH]\exists y(M(y) \land \lnot W(y))[/MATH] 1. [MATH]\exists y(M(y) \land \lnot W(y))[/MATH] by (B) 2. [MATH]\lnot (y) \lnot (M(y) \land \lnot W(y))[/MATH] by (1) 3. [MATH]\lnot (y) (\lnot M(y) \lor W(y))[/MATH] by (2) 4. [MATH]\lnot (y) (M(y) \rightarrow W(y))[/MATH] by (3) 5. [MATH] \lnot (y)(M(y) \rightarrow W(y)) \rightarrow \lnot \exists x(F(x) \land S(x))[/MATH] by (A) 6. [MATH]\lnot \exists x (F(x) \land S(x))[/MATH] by (4), (5) MP 7. [MATH] (x) \lnot (F(x) \land S(x))[/MATH] by (6) 8. [MATH](x)(\lnot F(x) \lor \lnot S(x))[/MATH] by (7) 9. [MATH](x)(F(x) \rightarrow \lnot S(x))[/MATH] by (8)
(A) [MATH]\exists x(F(x) \land S(x)) \rightarrow (y)(M(y) \rightarrow W(y))[/MATH](B) [MATH]\exists y(M(y) \land \lnot W(y))[/MATH] 1. [MATH]\exists y(M(y) \land \lnot W(y))[/MATH] by (B) 2. [MATH]\lnot (y) \lnot (M(y) \land \lnot W(y))[/MATH] by (1) 3. [MATH]\lnot (y) (\lnot M(y) \lor W(y))[/MATH] by (2) 4. [MATH]\lnot (y) (M(y) \rightarrow W(y))[/MATH] by (3) 5. [MATH] \lnot (y)(M(y) \rightarrow W(y)) \rightarrow \lnot \exists x(F(x) \land S(x))[/MATH] by (A) 6. [MATH]\lnot \exists x (F(x) \land S(x))[/MATH] by (4), (5) MP 7. [MATH] (x) \lnot (F(x) \land S(x))[/MATH] by (6) 8. [MATH](x)(\lnot F(x) \lor \lnot S(x))[/MATH] by (7) 9. [MATH](x)(F(x) \rightarrow \lnot S(x))[/MATH] by (8)
