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Unformatted text preview: by F1. Proved. Problem 3. o Vx Vy Ez P(x,y,z) o Vx Vy Vz Vx ((P(x,y,z) and P(x,y,w)) => E(z,w)) o Vx Vy Vs Vz Va Vt Vb ((P(x,y,s) and P(s,z,a) and P(y,z,t) and P(x,t,b)) => E(a,b) Problem 4. o P(a, f(a)) and P(b, f(b)) = P(1, f(1)) and P(2, f(2)) = P(1, 2) and P(2, 1) = T and F = F o Vx Ex P(y,x) Consider y=1 then for x = 1, P(y, x) = P(1,1) = true Consider y=2 then there does not exist x such that P(2, x) = true So Vx Ex P(y,x) is false under this interpretation o left as an exercise...
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 Spring '09
 Nhut

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