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

Question

Prove that the following arguments are standard by constructing metaphorical proof

$(A \leftrightarrow B) \rightarrow (D \leftrightarrow E)$

$(D \leftrightarrow E) \rightarrow\ \sim H$

$\sim\ \sim H$

$\sim (A \leftrightarrow B) \rightarrow F$

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

✓

Answer

$(1)\ (A\ \leftrightarrow\ B) \ \rightarrow\ (D\ \leftrightarrow\ E)$	$P$
$(2)\ (D\ \leftrightarrow )\ S\ \sim\ H$	$P$
$(3)\ \sim\ \sim\ H$	$P$
$(4)\ \sim\ (A\ \leftrightarrow\ B)\ \rightarrow\ F$	$P/\ (F\ v\ G)\ \&\ \sim\ \sim\ H$
$(5)\ \sim\ (D\ \leftrightarrow\ E)$	$2,3, MT$
$(6)\ \sim\ (A\ \leftrightarrow \ B)$	$1, 5, MT$
$(7)\ F$	$4, 6, MP$
$(8)\ F\ v\ G$	$7,$ Add.
$(9)\ (F\ v\ G)\ \&\ \sim\ \sim\ H$	$8, 3,$ Conj.

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