¬(¬p) ≡ p
To prove that the statement ¬(¬p) ≡ p is true, we can use the laws of negation in propositional logic
To prove that the statement ¬(¬p) ≡ p is true, we can use the laws of negation in propositional logic.
First, let’s analyze ¬(¬p) on the left-hand side of the equation. The outer negation symbol ¬ applied to the expression ¬p indicates the logical negation of ¬p. By applying the negation law, we can rewrite this as p.
Therefore, ¬(¬p) is equivalent to p.
On the right-hand side of the equation, we have p. Since p is the same as p itself, we can conclude that ¬(¬p) ≡ p.
In simpler terms, this equation states that “the negation of the negation of p is equivalent to p.”
To understand this better, let’s consider the possible truth values of p:
1. If p is true, then ¬(¬p) means the negation of negation of true, which gives us true. So, p and ¬(¬p) are both true in this case.
2. If p is false, then ¬(¬p) means the negation of negation of false, which gives us false. So, p and ¬(¬p) are both false in this case.
For every possible truth value of p, ¬(¬p) and p have the same truth values. Hence, we can confirm that ¬(¬p) ≡ p for all truth values of p.
This conclusion demonstrates the logical equivalence of ¬(¬p) and p.
More Answers:
A Logical Equivalences Proof: Breaking Down the Given Statement and Proving its TruthUnderstanding the Logical Equation p ∧ ¬p ≡ F: A Step by Step Analysis using Basic Laws of Logic
Proving the Equality p ∧ p ≡ pp ∨ p ≡ p with Boolean Algebra Simplification