What is conjunction?

Consider the following three statements:

$\left(A\right)$ If $3+3=7$ then $4+3=8$

$\left(B\right)$ If $5+3=8$ then earth is flat.

$\left(C\right)$ If both $\left(A\right)$ and $\left(B\right)$ are true then $5+6=17.$

Then, which of the following statements is correct?

Consider the following two propositions :
$P_1$: $~\left(p\to ~q\right)$
$P_2$: $\left(p\wedge ~q\right)\wedge \left(\left(~p\right)\vee q\right)$

If the proposition $p\to \left(\left(~p\right)\vee q\right)$ is evaluated as FALSE, then

Consider the following three statements:

$P:5$ is a prime number

$Q:7$ is a factor of $192$

$R: \mathrm{LCM}$ of $5$ and $7$ is $35$

Then the truth value of which one of the following statements is true?