Question 483530: if p is true, q is false, and r is true, find the truth value of the statement.(r → ∼p) ∧ (q → ∼r)
Answer by tinbar(133)   (Show Source):
You can put this solution on YOUR website! let's do the left side of the conjunction first: r is true, p is true, so not p is false. So we need to check whether T->F is true. By checking basic truth tables, you will find this assignment is false, so the left side of the conjunction is false. Now the right side: q is false, and r is true, so not r is false. We need to check whether F->F is true. It is the case that this is true. So we have one side false and one side true of a conjunction, therefore the entire in conjunction is false.
Note: We could have determined the final answer as soon as we'd done the left side since we knew it was false. In a conjunction if one side is false, regardless of the outcome of the other side the entire conjunction will be false.
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