GO Classes Weekly Quiz 5 | Propositional Logic | Question: 7

Answer 1

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. 

Answer 2

If F1 ^ F2 → F3 = False, (i.e contradiction)

then, it must be T → F = F.

So, F1 ^ F2 = T and F3 = F.

Thus options (a), (b) and (c ) are correct answers to this question.

 

After watching Deepak sir’s explanation, I thought of changing my answer here so that nobody reading the discussion on this beautiful question gets confused.

Basically, we can say a propositional variable is tautology ONLY WHEN all the values of it are True. 

Now, for F1^F2 to be True, both must be true and it is the ONE AND ONLY case possible for the value of the conjunction to be True.

 

Please check the discussion on https://gateoverflow.in/400763/go-classes-weekly-quiz-5-propositional-logic-question-16 → this question, to get a better understanding of the correct approach to solve this question.