Question

Show that $\neg \left(\neg \text{p}\right)$and pare logically equivalent.

Short answer

The logical equivalence between $\neg \left(\neg \text{p}\right)$ and P can be verified with the help oftruth tables.Prepare a truth table for every statement and also take different values of P and Q inputssuch as every possible combination of T and F tocheck the result for their equivalence.

Step-by-step solution

Definition of Logical equivalence

In propositional logic, logical equivalenceis a form of connection between two facts or statements.

Proof of logical Equivalence using Truth Table

The two logical expressions are given $\neg \left(\neg \text{p}\right)$and P such as they are logically equivalent if their truth values agree for all possible inputs.

Prepare a truth table for $\neg \left(\neg \text{p}\right)$

Truth Table

From the truth table, it is true that .$\neg \left(\neg \text{p}\right)\equiv P$

Therefore, it has been proved that $\neg \left(\neg \text{p}\right)$and P islogically equivalentwith the help of the truth table.