Statement, Negation

Statement, Negation

How to solve the truth values of a statement and its negation problems: examples and their solutions.

Example 1

p represents the given statement: p: 5 is a positive number. For each sentence given in symbolic form: a. Write a complete sentence. b. Find the truth value. 1. ~p 2. ~(~p)

A statement is a sentence that is either true or false.

p: 5 is a positive number.
The truth value of p is true.

~p is called 'not p'.
So p and ~p have the opposite truth values.

~p: 5 is not a positive number.

p is true.
So ~p is false.

~(~p) has two ' ~ '.
So just like -(-p) = +p,
~(~p) = p.

~(~p) = p: 5 is a positive number.

p is true.
So ~(~p) is true.

Example 2

q represents the given statement: q: 1 + 1 = 3. For each sentence given in symbolic form: a. Write a complete sentence. b. Find the truth value. 1. ~q 2. ~(~q)

p: 1 + 1 = 3

p is false.

~p: 1 + 1 3

p is false.
So ~p is true.

~(~p) = p: 1 + 1 = 3

p is false.
So ~(~p) is false.