Question

Create a truth table for this statement. (p^q) ->r Choose the answer that matches correct final column of the table. Use the following to help you organize your thoughts before answering. You may not need all the provided columns. р T q T T T T T F F T F T F T F T F T T F F F F F F

Answer 1

Before We create truth table for ($19)>8 let's have a look at the following definitions Definition ! ÞXq is F (ie false) if any one of eq is For or both Another definition: Paq is t (True) if both are T. Definition 2: þq is F only when bis Tli.e true) and q is F (i e False) Truth table for (P18) : p q r paq ($19) Т ТТ T T TJ F ТЕТ To It T l T 7 F T F F F F F C F T L LL FT F T F T

Explaredo Observe the truth values in the column 4: The first truth value is T Reasons & ke notice that is I and QIST. By definition, if both b, q are T then PXq is T. The third truth value is F Reason: We notice that p is T and q, is F. By definition, if any one of piq is F then Paq is F. The fifth truth value is f Reason: We can notice that both peq are F. So by definition, PAQ is F

PAq is T The and observe the truth values in the last columns The 1st truth value is T Reason: We notice that pag is T and r ist. But by definition (P19) is F only when and r is F. truth value is F. Reason: From the table, we notice that Paq is T and r is By definition (P190 >r will be F. The #5th truth value is T Reason: From the table, we notice that Þaq is F and r is F. But by definition, $19) >r will be F #only when paq is 1 and q is F.