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

Question

Prove that the following arguments are standard by constructing metaphorical proof

$(M \leftrightarrow N) \rightarrow O$

$\sim A\ v\ (B\ \&\ D)$

$B \rightarrow (O \rightarrow P)$

$\sim \sim A$

$\therefore (M \leftrightarrow N) \rightarrow P$

✓

Answer

$(1)\ (M \leftrightarrow N) \rightarrow O$	$P$
$(2)\ \sim\ A\ v\ (B\ \&\ D)\ \sim $	$P$
$(3)\ B\ \rightarrow (O\ \rightarrow\ P)$	$P$
$(4)\ \sim\ A$	$P/ \therefore\ \sim (M \leftrightarrow N) \rightarrow P$
$(5)\ B\ \&\ D$	$2, 4, DS$
$(6) \ B$	$5,$ Simp.
$(7)\ 0\ \rightarrow\ P$	$3, 6, MP$
$(8)\ (M\ \therefore\ N) \rightarrow\ P$	$1, 7, HS$

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