If a polygon is a pentagon, then it has five sides.
Remember that conditional statement combines a hypothesis p and a conclusion q. A conditional statement can be written as an if-then.
p→ q ⇒ If p, then q
Therefore, whatever comes after if in our statement is the hypothesis, and what comes after then is the conclusion.
Extra
More about Statements
The negation of a statement is the opposite of the original statement. To write a negation of a statement p, we need to write the symbol for negation (~) before the letters.
~ p → Not p
We can also write the converse, contrapositive, and the inverse of a conditional statement. Let's see the differences in the following table!
Related Conditionals
Name
Words
Symbol
Converse
If p, then q.
p → q
Inverse
If q, then p.
~ p → ~ q
Contrapositive
If not q, then not p.
~ q → ~ p
A conditional statement can be true unless a true hypothesis leads to a false conclusion. To see all the possibles cases, we can use a true table.
Conditional Statement
p
q
p ⇒ q
T
T
T
T
F
F
F
T
T
F
F
T
Notice from the table that a conditional statement is false only when the hypothesis is true and the conclusion false. In any other case, a conditional statement is true.
