Understanding Logic

$8\mathrm{.}5$ Exercises

A$.$ Prove the following arguments valid using the indirect proof of validity.

$(1)$ Asup$(BvvC)$

$(2)CA\frac{,}{}A$

Example Solution:

$(1)$ Asup$(BvC)$

$(2)CA$

$(3)B\frac{,}{}A$

$\backslash$table$[[,|(4)A,$AIP$],[,|(5)$ A$,3$ DN$],[,(6(6)BvC,1,5$ MP$],[,|(7)C,6,3$ DS$],[,|(8)A,2,7$ MP$],[,|(9)A*A,5,8$ Conj$],[(10),,$IP $4-9],[(11)A,,10,$ DN$]]$

$(1)(R*B)T$

$(2)(KvvY)sup(R*B)$

$(3)(K*T)*Y$

$\frac{?}{?}T$

$(1)(WsupS)*R$

$(2)(ST)*J$

$(3)TS\frac{,}{}W$

$(1)MsupO$

$(2)MvvW$

$(3)WN\frac{,}{\text{:}}.OvN$

$(1)[Avv(FvvK)]$

$(2)$ AvvC

$/$ :$.C$

$(1)$ R v $$T

$(2)$ Tsup$(JsupS)$

$(3)(SvvR)$

$1J$