QUESTION $2$

$10$ points

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Recall the procedure for building truth tables. Then build truth tables to determine the validity of the following arguments from the list below: $10,11,15,17.$ Choose the answer that correctly identifies the valid and invalid arguments.

$2.$ PsupQ $Q$

$\frac{?}{?}P$

$3.$ PsupQ QsupR

$4.PvvQP$

$\frac{?}{\text{P}\text{s}\text{u}\text{p}\text{R}}$

$/$Q

$15.(PsupQ)*(RsupS)PvvR$

$6.P*Q$

$7.PQ$

$8.P$

$9.R-=S$

$10.(R*S)supS$

$11.P-=(PvvS)$

$P$

$12.(RsupS)R$

$13.(R*S)RsupP$

$14.(PvvQ)supS$

$15.(P*Q)vv(RsupP)QvvR$

$/$QvS $/$P

$\frac{?}{P}*Q/$PVQ

$/$ R

$16.[Svv(QvvR)]supQQ$

$R$

$/$S

$17.[(S*Q)*R]supQQ$

$R$

$1S$

$18.(SvvQ)sup(PvvR)Q$

$P$

$R$

Valid: $11$

Invalid: $10,15,17$

$2.$ Valid: $17$

Invalid: $10,11,15$

$3.$ Valid: $17$

Invalid: $10,11,15$

$4.$ Valid: $15$

Invalid: $10,11,17$

$5.$ None valid,

$6.$ Valid: $10,17$

Invalid: $11,15$

$7.$ Valid: $11$

Invalid: $10,11,15,17$

$8.$ Valid: $11,15$

Invalid: $10,17$

$9.$ Valid: $10$

Invalid: $11,15,17$

$10.$ All valid.