Proposition
A proposition is a statement that is either true or false, but not both.
A proposition must have a definite truth value.
Example:
- “\(5 + 3 = 8\)” → True
- “\(10\) is a prime number” → False
- “A triangle has three sides.” → True
Simple proposition
A simple proposition contains a single statement.
Example:
\(7\) is an odd number.
Compound proposition
A compound proposition is formed by combining two or more propositions using words such as and, or, if...then, if and only if
Example:
\(5\) is an odd number and \(5\) is a prime number.
Both statements are true, so the compound proposition is true.
Conditional proposition:
A statement of the form If P, then Q is called a conditional proposition.
Here: P → hypothesis/condition, Q → conclusion
The conditional proposition is written as P ⇒ Q and read as “P implies Q".
Example:
If a number is divisible by \(4\), then it is even.
Here P: The number is divisible by \(4\).
Q: The number is even.
Converse:
The converse of conditional statement is formed by swapping its hypothesis and its conclusion.
If original statement is "P implies Q"
Then converse is "Q implies P". Converse need not be necessarily true.
Example:
Statement: If a shape is a square, then it has four equal sides
Converse : If a shape has four equal sides then it is a square.