Conditional Statement Logical Equivalence Converse, Inverse and Contrapositive
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Conditional Statement
If two lines are at Right Angles, then they are Perpendicular
Logical Equivalence
- Statement If P then Q
- Converse If Q then P
- Inverse If not P then not Q
- Contrapositive If not Q then not P
- Biconditional P Q If & Only If (Iff)
Converse, Inverse, and Contrapositive of a Conditional Statement
- A conditional statement takes the form “If p, then q” where p is the hypothesis (antecedent) while q is the conclusion (consequent) . A conditional statement is also known as an implication.
- If statement is true, contrapositive is true
- If converse is true, inverse is true
- The conditional statement is logically equivalent to its contrapositive.
- Thus, p ⇾ q ≡ ~q ⇾ ~p.
- The converse is logically equivalent to the inverse of the original conditional statement. Therefore, q ⇾ p ≡ ~p ⇾ ~q.
Conditional
If Clouds, then Rain
Converse
If Rain, then Clouds
Inverse
If No Clouds, then No Rain
Contrapositive
If No Rain, then No Clouds
Two lines are at Right Angles If & Only If they are Perpendicular
✍ Manishika