Given formulas are $F_{1}$, $F_{2}$ and $F_{3}$
Question is saying that, $F_{1} \wedge F_{2} \rightarrow F_{3}$ is a contradiction.
Contradiction means it should be always FALSE.
See that $F_{1}$, $F_{2}$ and $F_{3}$ are formulas.
It can be any expression depending on some propositional variables like $p,q,….$
$p,q,…..$ |
$F_{1}$ |
$F_{2}$ |
$F_{3}$ |
$F_{1} \wedge F_{2}$ |
$F_{1} \wedge F_{2} \rightarrow F_{3}$ |
$……..$ |
$T$ |
$T$ |
$F$ |
$T$ |
$F$ |
|
$T$ |
$T$ |
$F$ |
$T$ |
$F$ |
|
$T$ |
$T$ |
$F$ |
$T$ |
$F$ |
So, From Truth Table we can observe that for truth values of $p,q,...$ variables the truth values of the Formulas $F_{1}, F_{2}, F_{3}$ are always $T, T, F$ respectively. Also, we are getting truth value of given expression always FALSE.
So, A; B; C are Correct.