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

Question

Prove that the following arguments are standard by constructing metaphorical proof

$(A\ v\ B) \rightarrow (D\ v\ C)$

$(E\ v\ F)\ v\ (A\ v\ B)$

$\sim (A\ v\ B)\ \&\ H$

$F \rightarrow (A\ v\ B)$

$\therefore [E\ \&\ \sim (A\ v\ B)]\ v\ S$

✓

Answer

$(1)\ (A\ v\ B) \rightarrow (D\ v\ C)$	$P$
$(2)\ (E\ v\ F)\ v\ (A\ v\ B)$	$P$
$(3)\ \sim (A\ v\ B)\ \&\ H$	$P$
$(4)\ F \rightarrow (A\ v\ B)$	$P/ \therefore [E\ \&\ \sim (A\ v\ B)]\ v\ S$
$(5)\ \sim (A\ v\ B)$	$3,$ Simp.
$(6)\ E\ v\ F$	$2, 5, DS$
$(7) \ \sim F$	$4, 5, MT$
$(8)\ E$	$6, 7 DS$
$(9)\ R\ \&\ \sim (A\ v\ B)$	$8, 5,$ Conj.
$(10)\ (R\ \&\ \sim (A\ v\ B)\ v\ S$	$9,$ Add.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "question To The Point .Marks)" from Rules of conjecture→Rules of conjecture — all question types→Philosophy STD 12 Arts question papers→Gujarat Board STD 12 Arts question papers→Gujarat Board question paper generator→

Similar questions

Prove that the following arguments are standard by constructing metaphorical proof

$P \rightarrow Q$

$\therefore (\sim P \& \sim R)\ v\ S$

Determine the validity of the following arguments using the direct method of truth table:
$P \rightarrow Q$
$Q \rightarrow P$
$\therefore P \leftrightarrow Q$

Determine the validity of the following arguments using the direct method of truth table:
$\sim A \leftrightarrow \sim B$
$\therefore\ \sim B \rightarrow \sim A$

All moderates are peaceful.
All dieters are peace loving.
All dieters are moderate.

Prove that the following arguments are standard by constructing metaphorical proof

$(J \rightarrow K)\ \&\ R$

$\sim P \rightarrow (A \rightarrow B)$

$P\ v\ (J\ v\ A)$

$\therefore K\ v\ B$

$(p\ V\ \sim\ \sim p)$

Prove that the following arguments are standard by constructing metaphorical proof

$T \rightarrow B$

$B \rightarrow ( \sim\ P \rightarrow\ \sim\ Q)$

$\sim\ P\ \&\ \sim\ R$

$\therefore\sim\ Q\ v\ X$

Prove that the following arguments are standard by constructing metaphorical proof

$(A \rightarrow B) \rightarrow R$

$R \rightarrow S$

$(A \rightarrow B)\ \&\ T$

All martyrs are patriots.
No traitor is a martyr.
No traitor is a patriot.

Prove that the following arguments are standard by constructing metaphorical proof

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

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

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

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

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

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