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

Question

Prove that the following arguments are standard by constructing metaphorical proof

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

$(A \rightarrow E)\ \&\ (D \rightarrow F)$

$(E\ v\ F) \rightarrow (B\ v\ D)$

$\sim B$

$D$

✓

Answer

$(1)\ B\ \&\ (A\ v\ D)$	$P$
$(2)\ (A \rightarrow E)\ \&\ (D \rightarrow F)$	$P$
$(3)\ (E\ v\ F) \rightarrow (B\ v\ D)$	$P$
$(4)\ \sim B$	$P/ D$
$(5)\ A\ v\ D$	$1,$ Simp.
$(6)\ A \rightarrow E$	$2,$ Simp.
$(7)\ D \rightarrow F$	$2,$ Simp.
$(8)\ E\ v\ F$	$6, 7, 5, CD$
$(9)\ B\ v\ D$	$3, 8, MP$
$(10)\ D$	$9, 4, DS$

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