Exercise i Which of the following implications are valid in intuitionistic logic ? Give either a tableau proof or a counterexample.
(a) cp a f ->■ f a (p
(b) f^((<pAf)vf)
(c) (-i//^ -9)    O i//)
(d) 9 —9
(e) ((cpAf)vf)^f
(f) —9 9
(g) <pv^<p
(h) -'(-'f a -.1//) -»• (^v f) (This one is tricky.)
(i) (p ->■ 3x<p (j) Vx<p 9
(k) VxR(x,x) ^ Vx3yR(f(x),y)
(1) 3x(<p v 1//) -»• 3x<p v 3xi//
(m) 3x<p v 3xi// -»• 3x(<p v f)
(n) Vx<p a Vxi// —>• Vx(<p a 1//)
(o) Vx(<p a 1//) -»• Vx<p a Vxi//
(p) VxV7[«jo(x) «-»• 9(7)] a 3x<p(x) -»• Vx<p(x)
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