Final answer:
The truth value of the given statement depends on the specific situations of Lindsey Vonn, Kevin Durant, Tom Brady, and Matt Ryan.
Step-by-step explanation:
To determine the truth value of the given statement, we need to break it down into logical operators and evaluate each part:
Let A be 'Lindsey Vonn plays professional tennis.'
Let B be 'Kevin Durant plays professional tennis.'
Let C be 'Tom Brady plays professional basketball.'
Let D be 'Matt Ryan plays professional basketball.'
The given statement can be translated as: ~(A ∧ B) ∧ (C ∨ D). Evaluating the statement step-by-step:
~(A ∧ B): This means it is not the case that both Lindsey Vonn and Kevin Durant play professional tennis.
So, if either one of them plays professional tennis or both of them don't, ~(A ∧ B) will be true.
(C ∨ D): This means either Tom Brady or Matt Ryan plays professional basketball. So, if either one of them plays professional basketball or both of them do, (C ∨ D) will be true.
~(A ∧ B) ∧ (C ∨ D): Combining the two previous statements with the ∧ (and) operator, this expression evaluates to true if ~(A ∧ B) and (C ∨ D) are both true. Otherwise, it evaluates to false.
Therefore, the truth value of the given statement depends on the specific situations of Lindsey Vonn, Kevin Durant, Tom Brady, and Matt Ryan.