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

Question

Prove that the following arguments are standard by constructing metaphorical proof

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

$(Q \rightarrow T)\ \&\ (S \rightarrow P)$

$\sim T$

$\therefore \sim R\ \&\ \sim T$

✓

Answer

$(1)\ (P \rightarrow Q)\ \&\ (R \rightarrow S)$	$P$
$(2)\ (Q \rightarrow T)\ \&\ (S \rightarrow P)$	$P$
$(3)\ \sim 7$	$P/ \therefore \sim R\ \&\ \sim T$
$(4)\ Q \rightarrow T$	$2,$ Simp.
$(5)\ \sim Q$	$4, 3, MT$
$(6)\ P \rightarrow Q$	$1,$ Simp.
$(7)\ \sim P$	$6, 5, MT$
$(8)\ S \rightarrow P$	$1,$ Simp.
$(9)\ \sim S$	$8, 7, MT$
$(10)\ R \rightarrow S$	$1,$ Simp.
$(11)\ \sim R$	$10, 9, MT$
$(12)\ \sim R\ \&\ \sim T$	$11, 3,$ Conj.

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