GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 10

Answer 1

here answer should be ABCD but given is BCD

A because FVQ so if atleast one of them is true then output is true ..

Comments

option A is false when F: q and G: ~q.

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@Suraj Reddy How?

$F \vee G$ is Tautology ↔ $F$ is True or $G$ is True. (This is a True Statement)

Proof:-

Direct: $F \vee G$ is Tautology → $F$ is $T$ or G is $T$

$F \vee G$ can be a Tautology only if atleast one of $F$ or $G$ is $T$.

Indirect: $F$ is $T$ or $G$ is $T$ → $F \vee G$ is Tautology

$ \implies F$ is $T$ or $G$ is $T$

If anyone is true, definitely $F \vee G$ is going to be $T$.

@Deepak Poonia Sir, please have a look. Option A should also be correct.

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@Abhrajyoti00

In my counter-example, F V G is a tautology. But neither F nor G is a tautology.

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@Suraj Reddy What is the value of q ?

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@Abhrajyoti00 q is a propositional variable that can be true or false and F is a propositional formula as mentioned in the question that is made from a bunch of propositional variables and logical connectives. For simplicity, F is assumed to be made up of just one propositional variable.

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So if you take q = True, ~q has to be False right?

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Find the Detailed Video Solution: Propositional Formula Question - Complete Analysis

Detailed Text Explanation is HERE. 

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@Suraj Reddy So the reason option A is wrong is because it is mentioned as iff(if and only if) in the option.So in case the option had mentioned ‘if’ instead of ‘iff’,then option A would have been correct as well right?

Answer 2

Option A : F V G can be a tautology when F and G both are tautologies so the iff case is not valid : incorrect

Option B : F -> G is a tautology and F is a tautology which means T -> G = True only when G is a tautology : correct ans

Option C : (F -> G) or (F -> ~G) is a tautology : use By Case method, assume F = True then equation becomes G V ~G which will always be True : correct ans

Option D : (F -> G) and (F -> ~G) : use By Case method, assume F = True then equation becomes G ^ ~G which can never be True [unless in question given F is a contradiction] 

Hence F = False :: T V T will always be True : correct ans

 

Answers : B, C, D