why is this formula not logically valid?

Question

Let a unary predicate $R$ be the only nonlogical symbol of $L$. Then the formula $R(x) \rightarrow(\forall x) R(x)$ is not logically valid. How can I show that?

Answer 1

A formula is logically valid iff all structures and variable assignment functions satisfy the formula, and invalid iff there is at least one counter model + assignment under which it is false.
So to ensure that $R(x)$ is true under a certain assignment and $\forall x R(x)$ false, you just need to define the model such that $R$ is true of one object and false of another one, and specify the relevant variable assignment.

Answer 2

Hint:

Consider a domain $\{a,b\}$ where $R(a)$ and $\lnot R(b)$ are true.

What is the truth value of $R(a) \to \forall x . R(x)$?

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I hope this helps ^_^