6.5. Question 4

Try these first

1. 1.

   Translate 'You drive over 65 miles per hour' into propositional logic.

   Hint

   Identify the propositional variable.

2. 2.

   What is the negation of 'You get a speeding ticket'?

   Hint

   Think about what negation means.

3. 3.

   What symbol denotes negation in propositional logic?

   • ¬
   • ∧
   • ∨

   Hint

   Think about the phrasing 'not p'.

4. 4.

   Is the statement 'If you do not drive over 65 MPH, then you will not get a speeding ticket' logically equivalent to 'You will get a speeding ticket only if you drive over 65 mph'?

   • True
   • False

   Hint

   Evaluate the conditions of each implication carefully.

5. 5.

   Create a contrapositive for the statement: 'If you do not enter a valid password, then you do not have access.'

   Hint

   Remember, contrapositive swaps hypotheses and conclusions.

6. 6.

   Analyze the expression 'p ∨ ¬p' for its truth values and logical equivalence.

   Hint

   Evaluate the possibilities of p being true or false.