Translate the following sentences into predicate logic language. Use the following translation key:
a ~ Anne
b ~ Bob
M(x) ~ x is male
G(x,y) ~ x is married to y
C(x,y) ~ x is a child of y
a) Anne has exactly two kids, both of which are married to Bob
b) All grandparents have or only daughters, or exactly two sons, or they are childless.
I'm struggling with this, especially the last sentence. Is this correct?
a) $\exists x \exists y (C(x,a) \wedge C(y,a) \wedge \neg x=y \wedge \neg \exists z ( C (z,a) \wedge \neg z =x \wedge \neg z = y) \wedge G(x,b) \wedge G(y,b)).$
b) $\forall x \exists y \exists z ( C(y,x) \wedge C(z,y) \implies (\forall u (C(u,x) \implies \neg M(u)) \vee (\exists v \exists w (C(v,x) \wedge C(w,x) \wedge M(v) \wedge M(w) \wedge \neg v = w \wedge \neg \exists s (C(s,x) \wedge \neg s = v \wedge \neg s = w))) \vee \neg \exists t (C(t,x))))$
My head is exploding right now. xP I'm not sure about the brackets and the quantifiers.
Thanks is advance.