Question 483530
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.