Hello, I have the following problem, but I don't know how to approach this.

Given the domain: {a, b, c},

and the following predicates:

P is interpreted as {(a,b), (b,c), (b,b)}

Q is interpreted as {(a,a), (c,c)}

Find the truth values of the following formulae under this interpretation,briefly justifying your answer:

(a) ∀x(P(x,c)⇒Q(x,x))

(b) ∀x∃y(P(x,y)∨Q(x,x))

(c) ∃x(Q(x,x)⇒∀y(P(c,y)∨P(x,y)))

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So far, I have attempted to solve this problem by renaming the domain values and predicates, to make it "easier" to comprehend.

Domain: {ann, bob, carmen}

Predicates:

P- Parties{(ann,bob), (bob, carmen), (bob, bob)}

Q- Questions{(ann, ann),(carmen, carmen)}

(a) For all people x, it is the case that x parties with carmen given that x questions himself/herself.

We see that this is false, since the only person who parties with carmen does not question himself.

This seems like a rather complicated and not mathematical approach. How can I approach this problem in a different way?