Question

2. Find a model for each of the following wffs. a. 3x (p(x) — 9(x))^VX - p(x) b. 3x Vy p(x, y) ^ 3x Vy - p(x, y)

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Answer 1

Answers @ 3x (PCW) ->9(29)1trx -D COD let the domain be D-{a,b} p(x) and qa) be such that let pla) =E, Pb) = F gea) -T, 9(0)=7 Then, For a=a, p(x) g(x) (since I T ] Also, for a=a, b - P(x) [since pla)= F = p(b) and JF=7] Hence, Ix (Poo 9(x)) A Vx ~P(x). ® For example, D={1, 2}, povex is greater than 3, 9(1)x is positive let the domain be D-{a,b} let plax, y) be such that Pla, a) = T, peablet

p(b,a) = F , pcb, b) = F. Then, for x-a, Hy pex, y) [since pla,al=T= p (a, b)] Also, for 2 =b, Ay - pcx, y) [since plbia)=F=p(6.b)] Hence, Jaty pcx, y) ^ J x Hy 7p (2,4). for example, D={1,2}; puyj: is odd.