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

Question

Prove that the following arguments are standard by constructing metaphorical proof

$(P\ \&\ Q) \rightarrow S$

$S \rightarrow ( \sim L \rightarrow \sim N)$

$\sim L\ \&\ \sim N$

$P\ \&\ Q$

$\therefore\sim N\ v\ F$

✓

Answer

$(1)\ (P\ \&\ Q ) \rightarrow S$	$P$
$(2)\ S \rightarrow 5( \sim\ L \rightarrow \sim\ N)$	$P$
$(3)\ \sim\ L\ \&\ \sim\ N$	$P$
$(4)\ P\ \&\ Q$	$P/ \therefore \sim\ N\ v\ F$
$(5)\ (P\ \&\ Q) \rightarrow ( \sim L \rightarrow \sim N)$	$1, 2, HS$
$(6)\ \sim L \rightarrow \sim N$	$5, 4, MP$
$(7)\ \sim L$	$3,$ Simp.
$(8)\ \sim N$	$6, 7, MP$
$(9)\ \sim\ N\ v\ F$	$8,$ Add.

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