Logicians say that validity is monotonic: if a set of assumptions entails

something, then adding more assumptions won't change this fact. To show

this, suppose that we have two sets of well formed formulas, $$ and $,$ such

that

$($a$)$ every formula in $$ is also in $,$ and

$($b$)|==A.$

Explain why it must also be the case that $|==A.$

Using the result above, explain why a logical truth $($a semantic conse$-$

quence of no assumptions, i$.$e$.,\frac{O}{|}==A)$ is also a semantic consequence of

every set of formulas.