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

Question

Prove that the following arguments are standard by constructing metaphorical proof

$\sim\ L\ \rightarrow\ \sim\ N$

$(A\ v\ B)\ \rightarrow\ Q$

$Q\ \rightarrow\ [(S\ \&\ T) \rightarrow\ P]$

$(S\ \&\ T)\ v\ \sim\ L$

$A\ v\ B$

$\therefore\ (P\ v\ \sim\ N)\ \&\ Q$

✓

Answer

$(1)\ \sim\ L\ \rightarrow\ \sim\ N$	$P$
$(2)\ (A\ v\ B)\ \rightarrow\ Q$	$P$
$(3)\ Q\ \rightarrow\ [(S\ \&\ T)\ \rightarrow\ P)$	$P$
$(4)\ (S\ \&\ T\ v\ \sim\ L$	$P$
$(5)\ A\ v\ B$	$P/\ \therefore\ (P\ v\ \sim\ N)\ \&\ Q$
$(6)\ Q$	$2, 5, MP$
$(7)\ (S\ \&\ T)\ \rightarrow\ P$	$3, 6, MP$
$(8)\ P\ v\ \sim\ N$	$7, 1, 4, CD$
$(9)\ P\ v\ \sim\ N$	$8, 6,$ Conj.

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