First slide

Introduction to mathematical reasoning

Question

Which of the following is wrong statement?

Moderate

A

$p \to q$ is logically equivalent $~ p \lor q$
B

If the truth values of p, q, r are T, F, T respectively, then the truth value of $(p \lor q) \land (q \lor r)$ is T
C

$~ (\lor q \lor q \lor r) ≅\sim p \land ~ q \land ~ r$
D

The truth value of $p \land ~ (p \lor q)$ is always T

Solution

The truth tables of $p \to q and ~ p \lor q$ are given below
Clearly, truth tables of $p \to q and ~ p \lor q$ are same. So, $p \to q$ is logically equivalent to $~ p \lor q$ . Hence, option (a) is correct.
If the truth value of p, q, r are T, F, T respectively, then the truth values of p v g and q v r are each equal to T.
Therefore, the truth value of $(p \lor q) \land (q \lor r)$ is T. Hence, option (b) is correct.
We know that, $~ (p \lor q \lor r) ≅ (~ p \land ~ q \land ~ r)$
So, option (c) is correct.
If p is true and q is false, then $p \lor q$ is true.
Consequently $~ (p \lor q)$ is false and hence $p \land ~ (p \lor q)$ is
false.
Hence, option (d) is wrong.

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