# Suppose the following two statements (x=a) ∨ (x ne a) is it true or false? I know that its false when only both operators are false, but I don't know in this case if it can be the case

Suppose the following two statements $\left(x=a\right)\vee \left(x\ne a\right)$ is it true or false? I know that its false when only both operators are false, but I don't know in this case if it can be the case
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Step 1
For any sentence $P,P\vee \mathrm{¬}P$ is a tautology and is therefore true.
Step 2
Consider the two possible truth values of P. Normally your sentence would have an implied quatification of $\mathrm{\forall }x,a$ before it to bind the variables.
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Step 1
You can have $x=a$ or $x\ne a$. If $x=a$, then is true since $x=a$ is true; otherwise, if $x\ne a$, then is true.
Step 2
In general, given a property $P\vee \mathrm{¬}P$ is always true; similarly, $P\wedge \mathrm{¬}P$ is always false.