in exercises 7 30 either prove that the wff is valid argument or give an interpretation in which

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Question

In Exercises 17-30, either prove that the wff is a valid argument or give an interpretation in which it is false. 17. (x)[(AW) ^ (BWx)] - (x)[(aW) ^ (BWx)] 18. (x)[(R(x) V S6)] ~ (@)ROx) V (x)Sx) 19. (x)[(PGr) ^ (Bv)Ox;y)] - (x)[(y)[P(x) Q(x,y)]] 20. (Vx)[(P(x) ~> Qx)] ~ [(Vx)PGx) ~ (Vx)O(x)] 21. (Vx)P6))' ~ (Vx)P() ~ Q)) 22. [(Vx)P(x)- (Vx)Q(r)] - (Vx)[P(x) Q(x)] 23. (x)(Vy)Qr;v)- (Vypx)QGx; >) 24. (Vx)P(x) V (x)Q(x) - (Vx)P(x) V @(r)] 25. (Vx)[(AGx) ~ B6x)] ~ [(x)AW) ~ (x)B(x)] 26. (Vy)Qx; >) ~ P(x)] - [(vQx.") = P(x)] 27. [P(x) ~ (voxV)]-(v)[PWx) Q6x; V)] 28. (Vx)(P(r) V @)) ^(x)QW) (Ex)PGx) 29. (x)[P(x) Q(x)] ^(Vy)QW) R(y)]- (x)[PWx) R(x)] 30. (Vx)(Vy)[(PG) ^ Skx; y)) ~ Q)] (x)B(x) (Vx)(B() PGx)) (Vx)y)S6; V)~ ()O) pkasc #nswct number 30

          In Exercises 17-30, either prove that the wff is a valid argument or give an interpretation in which it is false. 
17. (x)[(AW) ^ (BWx)] - (x)[(aW) ^ (BWx)]
18. (x)[(R(x) V S6)] ~ (@)ROx) V (x)Sx)
19. (x)[(PGr) ^ (Bv)Ox;y)] - (x)[(y)[P(x) Q(x,y)]]
20. (Vx)[(P(x) ~> Qx)] ~ [(Vx)PGx) ~ (Vx)O(x)]
21. (Vx)P6))' ~ (Vx)P() ~ Q))
22. [(Vx)P(x)- (Vx)Q(r)] - (Vx)[P(x) Q(x)]
23. (x)(Vy)Qr;v)- (Vypx)QGx; >)
24. (Vx)P(x) V (x)Q(x) - (Vx)P(x) V @(r)]
25. (Vx)[(AGx) ~ B6x)] ~ [(x)AW) ~ (x)B(x)]
26. (Vy)Qx; >) ~ P(x)] - [(vQx.") = P(x)]
27. [P(x) ~ (voxV)]-(v)[PWx) Q6x; V)]
28. (Vx)(P(r) V @)) ^(x)QW) (Ex)PGx)
29. (x)[P(x) Q(x)] ^(Vy)QW) R(y)]- (x)[PWx) R(x)]
30. (Vx)(Vy)[(PG) ^ Skx; y)) ~ Q)] (x)B(x) (Vx)(B() PGx)) (Vx)y)S6; V)~ ()O) pkasc #nswct number 30

Added by Jennifer T.

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