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

Question

Prove that the following arguments are standard by constructing metaphorical proof

$(E\rightarrow F)\rightarrow H$

$\sim J\ v (F\ \&\ G)$

$F \rightarrow(H\rightarrow I)$

$\sim\ \sim J$

$G\ \&\ [(E\rightarrow F) \rightarrow I]$

✓

Answer

$(1)\ (E \rightarrow F) \rightarrow H$	$P$
$(2)\ \sim J\ v(F\ \&\ G)$	$P$
$(3)\ F \rightarrow (H \rightarrow I$	$P$
$(4)\ \sim\ \sim J$	$P/G[(E \rightarrow F) \rightarrow I]$
$(5)\ F\ \&\ G$	$2, 4, DS$
$(6)\ F$	$5,$ Simp.
$(7)\ H \rightarrow I$	$3, 6, MP$
$(8)\ (E \rightarrow F) \rightarrow I$	$1, 7, HS$
$(9)\ G$	$5,$ Simp.
$(10)\ G\ \&\ [(E \rightarrow F) \rightarrow I]$	$9, 8,$ Conj.

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