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

Question

Prove that the following arguments are standard by constructing metaphorical proof

$(P \leftrightarrow Q) \rightarrow (A \leftrightarrow B)$

$(R \ \&\ S)\ v\ (P \leftrightarrow Q)$

$(F \ \&\ D) \rightarrow \sim\ (R \ \&\ S)$

$(H \ \&\ G)\ v\ (F \ \&\ D)$

$\sim (H \ \&\ G)$

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

✓

Answer

$(1)\ (P \leftrightarrow Q)\ \rightarrow\ (A \leftrightarrow B)$	$P$
$(2)\ (R \ \&\ S)\ v\ (P \leftrightarrow Q )$	$P$
$(3)\ (F \ \&\ D)\ \rightarrow\ \sim\ (R \ \&\ S)$	$P$
$(4)\ (H \ \&\ G)\ v\ (F \ \&\ D)$	$P$
$(5)\ \sim\ (H \ \&\ G)$	$P/ (A\ \leftrightarrow\ B)\ v\ (B\ \leftrightarrow\ D)$
$(6)\ F \ \&\ D$	$4, 5, DS$
$(7)\ \sim\ (R \ \&\ S)$	$3, 6, MP$
$(8)\ P \leftrightarrow Q$	$2, 7, DS$
$(9)\ A\ \leftrightarrow\ B$	$1, 8, MP$
$(10)\ (A\ \leftrightarrow\ B)\ v\ (B\ \leftrightarrow\ D)$	$9,$ Add.

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