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

Question

Prove that the following arguments are standard by constructing metaphorical proof

$(K \rightarrow P) \rightarrow B$

$\sim R$

$(K \rightarrow P)\ v\ B$

$B \rightarrow R$

$\therefore\ \sim (K \rightarrow P)\ \&\ B$

✓

Answer

$(1)\ (K \rightarrow P) \rightarrow B$	$P$
$(2)\ \sim\ R$	$P$
$(3)\ (K \rightarrow P)\ v\ B$	$P$
$(4)\ B\ V\ R$	$P/ \therefore \sim (K \rightarrow\ P)\ \&\ B$
$(5)\ (K \rightarrow P) \rightarrow R$	$1, 4, HS$
$(6)\ \sim (K \rightarrow P)$	$5, 2, MT$
$(7)\ B$	$3, 6, DS$
$(8)\ \sim\ (K \rightarrow P)\ \&\ B$	$6, 7,$ Conj.

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