If $p$ and $q$ are two statements, then $(p \land q) \lor (q \leftrightarrow p)$ is

Question

The number of different permutations of all the letters of the word "PERMUTATION" such that any two consecutive letters in the arrangement are neither both vowels nor both identical is:

Answer 1

To determine whether the logical expression $(p \land q) \lor (q \leftrightarrow p)$ is a tautology, contradiction, or neither, we need to analyze it using truth tables. A tautology is an expression that is always true regardless of the truth values of its components, while a contradiction is always false.

$p$	$q$	$p \land q$	$q \leftrightarrow p$	$(p \land q) \lor (q \leftrightarrow p)$
T	T	T	T	T
T	F	F	F	F
F	T	F	F	F
F	F	F	T	T

Let's explain the truth table:

$p \land q$ is true only when both $p$ and $q$ are true.
$q \leftrightarrow p$ is true when $p$ and $q$ have the same truth value (both true or both false).
The expression $(p \land q) \lor (q \leftrightarrow p)$ combines these two using OR, so it is true if either of these sub-statements is true.

From the table, we observe:

The expression is true for (T, T) and (F, F) combinations of $p$ and $q$, and false for (T, F) and (F, T).

Thus, the expression $(p \land q) \lor (q \leftrightarrow p)$ is neither always true nor always false. Hence, it is neither a tautology nor a contradiction.

Therefore, the correct answer is neither tautology nor contradiction.

\(p\)	\(q\)	\(p \land q\)	\(q \leftrightarrow p\)	\((p \land q) \lor (q \leftrightarrow p)\)
T	T	T	T	T
T	F	F	F	F
F	T	F	F	F
F	F	F	T	T

If $p$ and $q$ are two statements, then $(p \land q) \lor (q \leftrightarrow p)$ is

Show Hint

The Correct Option is C

Solution and Explanation

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