Implications and Tautologies

Understanding implications and tautologies is crucial for mathematical proofs and logical reasoning.

Implications

Converse, Inverse, and Contrapositive

Example: Contrapositive

Tautology

Example: Tautology

Contradiction

Example: Contradiction

Logical Equivalence

Practice Problems

1. Write the converse and contrapositive of "If , then ."
2. Determine if is a tautology.
3. Prove that is a tautology.
4. Find the contrapositive of "If a number is divisible by 4, then it is even."