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

Question

Prove that the following arguments are standard by constructing metaphorical proof

$(P \rightarrow\ Q)\ \&\ R$

$E\ \&\ F$

$\therefore [(F\ \&\ G)\ \&\ R ]\ \&\ E$

✓

Answer

$(1)(P\ \rightarrow\ Q)\ \&\ R$	$P$
$(2)\ E\ \&\ F$	$P$
$(3)\ G$	$P/ \therefore\ [(F\ \&\ G)\ \&\ R]\ \&\ E$
$(4)\ F$	$2,$ Simp.
$(5)\ F\ \&\ G$	$4, 3,$ Conj.
$(6)\ R$	$1,$ Simp.
$(7)\ (F\ \&\ G)\ \&\ R$	$5, 6,$ Conj.
$(8)\ E$	$2,$ Simp.
$(9)\ [(F\ \&\ G)\ \&\ R]\ \&\ E$	$7, 8,$ Conj.

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