- conditional operation (⇒or →)
- conditional proposition
- conditional statement
- hypothesis (antecedent)
- conclusion (consequent)
- biconditional operation (⇔ or ↔)
- The conditional operation is like the "if then" in programming. It indicates that when a certain condition is met (called the hypothesis or antecedent) then a certain result must occur (called the conclusion or consequent).
- It's truth table looks like:
||p → q
- The biggest mistake students make with the conditional operator is marking it false when the condition is false. This is incorrect.
- The other way to think about the conditional operator is to remember that p ⇒ q ≡p q
- The other common mistake(s) people make are starting with a conditional statement and assuming its converse or inverse.
- An original conditional statement is only equivalent to it's contrapositive.
- The converse and inverse are equivalent TO EACH OTHER but are not the same as the original conditional or it's contrapositive.
- The biconditional operation is like a conditional statement that is true in both directions.
- That is, if p ⇒ q and q ⇒p then we say that p ⇔ q