2.2. Logical Operators and Propositions

Try these first

1. 1.

   Provide an example of a proposition.

   Hint

   Think of a statement that can be true or false.

2. 2.

   What symbol is used for the biconditional operator?

   Hint

   Consider how we express 'if and only if'.

3. 3.

   What is the definition of a tautology?

   Hint

   Consider statements with universal truth.

4. 4.

   True or False: The contrapositive of a statement is logically equivalent to the statement itself.

   • True
   • False

   Hint

   Draw out the implications to check for equivalence.

5. 5.

   Prove that (p ∨ ¬p) is a tautology using a truth table and alternatively using logical identities.

   Hint

   Evaluate the truth values stepwise.

6. 6.

   Provide a detailed proof for the equivalence of the two statements: p → q and ¬q → ¬p using a truth table and argumentation of logical identities.

   Hint

   Demonstrate with various cases.