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

Question

Prove that the following arguments are standard by constructing metaphorical proof

$G \rightarrow H$

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

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

$(S\ \&\ T)\ v\ G$

$A\ v\ B$

$(P\ v\ H)\ \&\ D$

✓

Answer

$(1)\ G \rightarrow H$	$P$
$(2)\ (A\ v\ B) \rightarrow D$	$P$
$(3)\ D \rightarrow [(S\ \&\ T) \rightarrow P]$	$P$
$(4)\ (S\ \&\ T)\ v\ G$	$P$
$(5)\ A\ v\ B$	$P/ (P\ v\ H)\ \&\ D$
$(6)\ D$	$2, 5, MP$
$(7)\ (S\ \&\ T)\rightarrow P$	$3, 6, MP$
$(8)\ P\ v\ H$	$7, 1, 4, CD$
$(9)\ (P\ v\ H)\ \&\ D$	$8, 6,$ Conj.

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~ { p$\leftrightarrow$[ ~p v ( q & ~ q)]}