Conditional
Definition
A conditional statement, also known as an implication, is a logical statement that has the form 'if p, then q' where p is the hypothesis and q is the conclusion. It is denoted as p → q and is true in all cases except when p is true and q is false.
5 Must Know Facts For Your Next Test
- The truth value of a conditional statement depends on the truth values of its components.
- A conditional statement is false only when the hypothesis (p) is true and the conclusion (q) is false.
- The contrapositive of a conditional statement (¬q → ¬p) always has the same truth value as the original conditional.
- The converse of a conditional statement (q → p) does not necessarily have the same truth value as the original conditional.
- In constructing truth tables, a conditional can be evaluated by examining each possible combination of truth values for p and q.
Review Questions
- When is a conditional statement false?
- What relationship does a contrapositive have with its original conditional?
- How do you denote a conditional statement symbolically?
"Conditional" appears in:
Related terms
Hypothesis: The first part of a conditional statement (p) which represents an assumed condition.
Conclusion: The second part of a conditional statement (q) which follows if the hypothesis holds true.
Biconditional: A logical connective between statements where both must be either true or false, denoted as p ↔ q.
