Predicte logic help

Arweee

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Apr 11, 2021
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I've attached the file need help for exams I'm preparing..IMG-20210411-WA0054.jpg
 

lex

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Mar 3, 2021
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419
(A) \(\displaystyle \exists x(F(x) \land S(x)) \rightarrow (y)(M(y) \rightarrow W(y))\)
(B) \(\displaystyle \exists y(M(y) \land \lnot W(y))\)

1. \(\displaystyle \exists y(M(y) \land \lnot W(y))\) by (B)
2. \(\displaystyle \lnot (y) \lnot (M(y) \land \lnot W(y))\) by (1)
3. \(\displaystyle \lnot (y) (\lnot M(y) \lor W(y))\) by (2)
4. \(\displaystyle \lnot (y) (M(y) \rightarrow W(y))\) by (3)
5. \(\displaystyle \lnot (y)(M(y) \rightarrow W(y)) \rightarrow \lnot \exists x(F(x) \land S(x))\) by (A)
6. \(\displaystyle \lnot \exists x (F(x) \land S(x))\) by (4), (5) MP
7. \(\displaystyle (x) \lnot (F(x) \land S(x))\) by (6)
8. \(\displaystyle (x)(\lnot F(x) \lor \lnot S(x))\) by (7)
9. \(\displaystyle (x)(F(x) \rightarrow \lnot S(x))\) by (8)
 
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