The mistake many make for this question is to consider $F_i$ as a propositional variable But it is actually a propositional formula.
For example, $F_1 $ can be $p \wedge q$, where $p,q$ are propositional variables.
To understand the difference between propositional variable and propositional formula, watch the following video:
https://youtu.be/PT7yn-k-wiU
Note that $F_1,F_2,F_3$ are propositional formulae, over some set of propositional variables which are not given in the question.
$\color{red}{\text{Think about this question:}}$ How many rows are there in the truth table of expression $F_1 \wedge F_2 \rightarrow F_3 $?
If your answer is $8$ then you have not understood the difference between a propositional formula and propositional variable. So, watch the above video.
Number of rows in the truth table of expression $F_1 \wedge F_2 \rightarrow F_3 $ will depend on the propositional variables of these propositional formulas $F_i.$ If $F_i$ is propositional formula over 10 propositional variables then number of rows in the truth table of $F_1 \wedge F_2 \rightarrow F_3 $ will be $2^{10}.$
If each $F_i$ is propositional formula over propositional variables $p,q$ then number of rows in the truth table of $F_1 \wedge F_2 \rightarrow F_3 $ will be $4$ only, not 8.
For example, $F_1 = \neg p, F_2 = p \wedge q, F_3 = p \rightarrow q$ will satisfy all the conditions given in the question. But here, truth table of $F_1 \wedge F_2 \rightarrow F_3 $ will have only 4 rows, not 8, as the number of rows is determined by propositional variables, not by propositional formulas.
The $\color{red}{\text{Detailed Video Solution}}$ of this GATE question, MUST watch to get conceptual clarity:
https://youtu.be/85YwyEd_iaI
$\color{Purple}{\text{Some Variations:}}$
Variation 1: https://youtu.be/Gc40DqkSK3w
Variation 2: https://youtu.be/0TvPUMrtQ_8
Variation 3: https://youtu.be/Bw5At8oLeRY
So, answer will be Option B But the method of some students is Not correct.
NOTE that the mistake of Not understanding the difference between propositional variable and propositional formula can sometimes give you wrong answer and hence, negative marks.
For example, Consider the statements:
Let $\text{A, B}$ be two propositional formulas.
Which of the following assertions is/are true?
- If $\text{A} \wedge \text{B}$ is contradiction, then $\text{A}$ is contradiction or $\text{B}$ is contradiction.
- If $\text{A} \rightarrow \text{B}$ is tautology, then $\text{A}$ is contradiction or $\text{B}$ is tautology.
- If $\text{A} \leftrightarrow \text{B}$ is tautology, then either both $\text{A, B}$ are tautology or both $\text{A, B}$ are contradictions.
- If $\text{A} \wedge \text{B}$ is tautology, then both $\text{A, B}$ are tautology.
You can think about this question.
Answer is Only statement 4 is True. Statement 1,2,3 are Not true.
Solution here: https://gateoverflow.in/526/gate-cse-1991-question-03-xii?show=396158#c396158