A conditional statement (if-then statement) consists of two parts:
- “if” clause (hypothesis or antecedent)
- “then” clause (conclusion or conclusion)
In this context, conditional statements are often considered as zero conditional. Other types exist and are described in English Conditionals.
Given a conditional statement “if 𝑃, then 𝑄”, we can create other related statements:
- conditional
- converse
- inverse
- contrapositive
- biconditional
Truth Table - Conditional Statements & Its Related Statements
|
Name |
antecedent (hypothesis) |
consequent |
conditional |
contrapositive |
converse |
inverse |
biconditional | |||
|---|---|---|---|---|---|---|---|---|---|---|
|
Syntax |
𝑃 |
𝑄 |
¬𝑃 |
¬𝑄 |
𝑃 → 𝑄 |
¬𝑃 ← ¬𝑄 |
𝑃 ← 𝑄 |
¬𝑃 → ¬𝑄 |
𝑃 ↔ 𝑄 | |
|
Given |
0 |
0 |
1 |
1 |
then |
1 |
1 |
1 |
1 |
1 |
|
0 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
0 | ||
|
1 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
0 | ||
|
1 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
conditional and contrapositive are tautologies
converse and inverse are tautologies