Discrete Math › Section B · Logic and proofs › Topic B.2
Implications and related statements
Nearly every theorem has the shape "if this, then that". This topic explains exactly when such an implication is true, why its truth table has to look the way it does, and how it relates to its converse, inverse and contrapositive.
In this topic
- The workhorse of mathematics
- The truth table
- Why a false hypothesis gives true
- Worked example: deciding implications
- Converse, inverse and contrapositive
- Which relatives agree
- Worked example: using the contrapositive
- If, only if, and if and only if
- Many ways to say it
- Worked example: what follows from a true implication
- Common mistakes to avoid
- Key takeaways
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