2.3. Standard Logical Equivalent Statements

Try these first

1. 1.

   Define a tautology and provide an example.

   Hint

   Think of statements that cannot be false.

2. 2.

   What is a contradiction?

   Hint

   Imagine statements that are logically impossible.

3. 3.

   What is a tautology?

   • A statement that is always true
   • A statement that is always false
   • A statement that can be true or false

   Hint

   Think of statements that cannot be false.

4. 4.

   True or False: A contradiction is a statement that can be true under certain conditions.

   • True
   • False

   Hint

   Consider the logical impossibility of such statements.

5. 5.

   Prove using logical identities that the expression '¬(p ∨ q) is equivalent to '¬p ∧ ¬q'.

   Hint

   Start by breaking each term down.

6. 6.

   Evaluate if 'p → q' and '¬q → ¬p' are logically equivalent using truth tables.

   Hint

   Construct truth tables for both implications and compare.