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

Question

Prove that the following arguments are standard by constructing metaphorical proof

$H \rightarrow (I \rightarrow J)$

$K \rightarrow (I \rightarrow J)$

$(\sim H\ \&\ \sim K) \rightarrow (\sim\ L\ v\ \sim M)$

$(\sim L \rightarrow\ \sim N)\ \&\ (\sim M \rightarrow \sim Q)$

$\sim (I \rightarrow J)$

$\sim N\ v\ \sim Q$

✓

Answer

$(1)\ H \rightarrow (I \rightarrow J)$	$P$
$(2)\ K \rightarrow (I \rightarrow J)$	$P$
$(3)\ (\sim H\ \&\ \sim K)\ \rightarrow (\sim\ L\ v\ \sim M)$	$P$
$(4)\ (\sim L \rightarrow \sim N)\ \&\ (\sim M \rightarrow \sim Q)$	$P$
$(5)\ \sim (I \rightarrow J)$	$P/ \sim N\ v \sim Q$
$(6)\ \sim L \rightarrow \sim N$	$4,$ Simp.
$(7)\ \sim M \rightarrow \sim Q$	$4,$ Simp.
$(8)\ \sim H ,$	$1, 5, MT$
$(9)\ \sim K$	$2,5, MT$
$(10)\ \sim H\ \&\ \sim K ,$	$8, 9,$ Conj.
$(11)\ \sim L v \sim M$	$3, 10, MP$
$(12)\ \sim N v \sim Q$	$6, 7, 11, CD$

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