There is first-order predicate formula
$$A = \forall a (\neg P(a,a))$$
$$B = \forall a \forall b \forall c (P(a,b)\wedge P(b,c)\Rightarrow P(a,c))$$
$$B'= \forall a \forall b \forall c (P(a,b)\wedge P(b,c)\Rightarrow \neg P(a,c))$$
$$C = \forall a \forall b (P(a,b)\Rightarrow \neg P(b,a))$$
Question: Show that $A \vee B \vee B' \vee C$ is not valid.
Valid means there is no truth assignment makes it false.
What I got understood are truth assignment and resolving $A\Rightarrow B$ to $\neg A \vee B$. But I can't understand how to implement '$\forall $' Universal notation into formula. And what happened when we use $P(a,b)$ instead of just $a$ or $b$.
So, can anyone solve above question with explaination step by step .
Many thanks. You're all legends!