Prove that the following arguments are standard by constructing m… - Vidyadip

Question

Prove that the following arguments are standard by constructing metaphorical proof

$(T\ \&\ P) \rightarrow \sim Q$

$\sim (T\ \&\ P) \rightarrow (R \rightarrow \sim Q)$

$(\sim S\ v\ R)\rightarrow\ \sim\ \sim Q$

$\sim S$

$\therefore \sim R\ \&\ \sim S$

✓

Answer

$(1)\ (T\ \&\ P) \rightarrow \sim Q$	$P$
$(2)\ \sim (T\ \&\ P)\rightarrow (R\rightarrow \sim Q)$	$P$
$(3)\ (\sim\ S\ v\ R) \rightarrow \sim \sim Q$	$P$
$(4)\ \sim s$	$P/\therefore \sim R\ \&\ \sim S$
$(5)\ \sim S\ v\ R$	$4,$ Add.
$(6)\ \sim \sim Q$	$3, 5, MP$
$(7)\ \sim (T\ \&\ P)$	$1, 6, MT$
$(8)\ R \rightarrow \sim Q$	$2, 7, MP$
$(9)\ \sim R$	$8, 6, MP$
$(10)\ \sim R\ \&\ \sim S$	$9, 4,$ Conj.

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