Final answer:
The correct logical expression for the statement 'Not both Jaguar and Porsche make motorcycles' is Option 1: ¬(J and P), which equates to the concept of mutually exclusive events in probability.
Step-by-step explanation:
The statement 'Not both Jaguar and Porsche make motorcycles' can be translated into a logical expression to indicate the relationship between these two manufacturers (J for Jaguar and P for Porsche) making motorcycles. When breaking down the logical expressions:
- Option 1: ¬(J and P) means 'It is not the case that both Jaguar and Porsche make motorcycles.'
- Option 2: (¬J and ¬P) means 'Neither Jaguar nor Porsche make motorcycles.'
- Option 3: ¬J or ¬P means 'Either Jaguar does not make motorcycles, or Porsche does not make motorcycles, or both.'
- Option 4: J or P means 'Jaguar makes motorcycles or Porsche makes motorcycles or both.'
The correct logical expression that matches the statement given is Option 1: ¬(J and P). This is because the statement specifies that not both companies make motorcycles, but it does allow for the possibility that one of them might. In terms of probability and events, this concept is similar to mutually exclusive events in probability where two events cannot both occur at the same time. For example, if A and C are mutually exclusive events, then the probability of A and C happening together, P(A AND C), is zero.