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

Question

Prove that the following arguments are standard by constructing metaphorical proof

$(P\ \&\ R)\ v\ \sim\ S$

$(P\ \&\ R)\ \rightarrow\ \sim\ T$

$M\ \rightarrow\ \sim\ \sim\ T$

$M$

$M\ \&\ \sim\ S$

✓

Answer

$(1)\ (P\ \&\ R)\ v\ \sim\ S$	$P$
$(2)\ (P\ \&\ R)\ \rightarrow\ \sim\ T$	$P$
$(3)\ M\ \rightarrow\ \sim\ \sim$	$P$
$(4)\ M$	$P/ M\ \&\ \sim\ S$
$(5)\ \sim \ \sim\ T$	$3, 4, MP$
$(6)\ \sim\ ( P\ \&\ R)$	$2, 5, MT$
$(7)\ \sim\ S$	$1, 6, DS$
$(8)\ M\ \&\ \sim\ S$	$4, 7,$ Conj.

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