GO Classes CS 2025 | Weekly Quiz 2 | Propositional Logic | Question: 13

Answer 1

 

Option A. $p \rightarrow (q \lor r) \equiv ((p \land \neg{q}) \rightarrow r) $

LHS:

$p \rightarrow (q \lor r)$ as p → q is same as $\neg{p} \lor q$

$ \neg{p} \lor q \lor r \\ $

$(p \land \neg{q}) \rightarrow r \\$ which is equivalent to RHS: $((p \land \neg{q}) \rightarrow r) $

Option B. $(p \land q) \lor r \not\equiv p \land (q \lor r)$ 

Option C. If $p \rightarrow q$ is False then p is True and q is False, then $q \rightarrow p$ is True as $False \rightarrow True$ is True

Option D. If $p \rightarrow q$ is True, then there 3 cases:

1. p is True, q is True
2. p is False, q is True
3. p is False, q is False

then for case 1, 3 $q \rightarrow p$ is True which contracts the statements saying it is False.

Therefore B and D are right options i.e they are false statements

Comments

A typo in the 5th line.

Answer 2

Option B , D are false.