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IX. CHAPTER NINE: PREDICATE LOGIC PROOFS. Prove valid:
(1) 1. ~ ( x)Ax (5) 1. ( x)[Ax (y)By]
/ (x)(Ax Bx) /(x)Ax (y)By
(2) 1. ~ Aa (6) 1. (x)Ax (y)By
/ ~ (x) (Ax Bx) /(x) [Ax (y)By]
(3) 1. ( x) (Ax Bx) (7) 1. (x)[(Ax Bx) Cx]
2. (x) [Ax (Cx Dx)] 2. ( y) ~ (~ Ay Cy)
/ (x) (Cx Dx) / ( x)(Ax Bx)
(4) 1. ~ ( x) ~ (~ Ax Bx) (8) 1. (x)(Ax Bx) ~ ( y)Cy
2. ~ (x)Bx / ~ (x)Ax 2. ~ (x) ~ Cx
/ ( x)(Cx Ax)
IX. SUGGESTED ANSWERS
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(1) 1. ~ ( x)Ax p
(4) 1. ~ ( x) ~ (~ Ax Bx)p
(6) 1. (x)Ax (y)By p
(8) 1. (x)(Ax Bx)