We learned about the statements which has a truth value. A statement can be True or False, but not both.
You can make new statements from simple statements, such a statement is called a Compound Preposition or a Compound Statement.
Let p and q be two statements,
p: The triangle has three equal sides.
q: The triangle is an equilateral triangle.
The compound statement is a statement using these two statements,
p ∧ q : The triangle has three equal sides and it is an equilateral triangle.
p ∨ q : The triangle has three equal sides and it is an equilateral triangle.
We constructed the compound statements using simple statements by using a connective.
A connective is a logical symbol that connects two simple statements.
The are many connectives, they are listed below
Note that there are rule associated with each of the logical connectives and we will discuss about them.
Truth Table for Compound Statements
Rule : If any of the variable p , q is True, then the statement is True, else it is false.
Rule : When both the variable p , q are True, then the statement is True, otherwise it is false.
p ⇒ q
Rule : The only case when the statement is False is when p is True and q is False, where p implies q Otherwise, the statement is True.
p ⇔ q
Rule : When both the variables p , q are same then the statement is True, Otherwise , it is False.