Question

How can we use double-negation deduction rule? For example, ~(~p) is the same as p.

Answer 1

The double-negation deduction rule states that ~(~p) is logically equivalent to p. This rule allows us to remove a double negation and obtain the original statement.

Step-by-step explanation:

The double-negation deduction rule states that if we have a statement that is negated twice, we can remove the double negation and obtain the original statement. In other words, ~(~p) is logically equivalent to p.

To understand this, let's break it down step-by-step:

1. The inner negation, ~p, negates the original statement p.
2. The outer negation, ~(~p), negates the negation of p.
3. When we have a negation of a negation, the two negations cancel each other out.
4. As a result, we are left with the original statement, p.

For example, if p represents the statement 'It is sunny today', then ~(~p) would mean 'It is not true that it is not sunny today,' which is equivalent to 'It is sunny today.'