1.4.3.2. Number of Distinct Logical Operators

Try these first

1. 1.

   What is a proposition?

   Hint

   Think of statements that can be verified to be true or false.

2. 2.

   Identify the logical operator: 'p AND q'.

   Hint

   What does AND mean in logic?

3. 3.

   How many distinct logical operators can be formed with two propositions?

   • 8
   • 10
   • 16

   Hint

   Focus on the combinations of true and false.

4. 4.

   An implication operator 'p → q' is false when:

   • p is true and q is false
   • p is false
   • Both p and q are false

   Hint

   Think about if-then statements.

5. 5.

   Prove using truth tables that the statement 'p AND (q OR r)' is equivalent to '(p AND q) OR (p AND r)'.

   Hint

   Start with evaluating the inner expressions first for easier organization.

6. 6.

   Given a truth table with rows for p and q defined, how would you formulate a new logical operator that outputs TRUE when both are FALSE?

   Hint

   Consider how negation would affect the truth table setup.