2.2.1. Bi-conditional Operator and Statement

Try these first

1. 1.

   Define a tautology and provide an example.

   Hint

   Think about statements that must be true in every scenario.

2. 2.

   What is the meaning of the bi-conditional operator?

   Hint

   Consider the mutual relationship between two conditions.

3. 3.

   What does the bi-conditional operator signify?

   • A conditional statement
   • Mutual exclusivity
   • Mutual dependence

   Hint

   Remember what 'if and only if' implies about the statements.

4. 4.

   True or False: A tautology is always false.

   • True
   • False

   Hint

   Reflect on the definition of tautology.

5. 5.

   Prove that the expression 'not (p or q)' can be simplified to 'not p and not q'. Use logical identities to demonstrate your reasoning.

   Hint

   Utilize negation rules to manipulate the expression.

6. 6.

   Consider the statements X: 'p → q' and Y: 'not q → not p.' Prove that X and Y are logically equivalent.

   Hint

   Analyze how truth values align in both scenarios.