6.7.1. Part A

Try these first

1. 1.

   What is the negation of the statement 'it is raining'?

   Hint

   Think of the opposite of raining.

2. 2.

   If p is true, what is the truth value of ¬p?

   Hint

   Remember that negation flips the truth value.

3. 3.

   What does ¬p represent?

   • You drive over 65 mph
   • You do not drive over 65 mph
   • You will not get a ticket
   • You will get a ticket

   Hint

   What is the opposite of the statement?

4. 4.

   If p → q is true, which of the following must also be true?

   • True
   • False

   Hint

   Think about when an implication can fail.

5. 5.

   Consider the logical statement 'the car accelerates only if the driver presses the pedal.' Can you express its contrapositive and check if they are equivalent?

   Hint

   Remember the relationship of implication and contrapositive.

6. 6.

   Devise a complex logical statement involving three propositions: driving over 65 mph (p), getting a ticket (q), and attending traffic school (r). Show its truth table.

   Hint

   Set up all combinations of truth values.