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

Question

Prove that the following arguments are standard by constructing metaphorical proof

$(A\ v\ B)\ \rightarrow\ [D\ \rightarrow\ (P\ \&\ \sim\ Q)]$

$(A\ \&\ J)\ \rightarrow [(P\ \&\ \sim\ Q)\ \rightarrow\ K]$

$(A\ \&\ J)\ \&\ (\sim\ K\ v\ D)$

$\therefore\ (D \rightarrow\ K)\ v\ \sim\ Q$

✓

Answer

$(1)\ (A\ V\ B)\ \rightarrow[D\ \rightarrow\ (P\ \&\ \sim\ Q)]$	$P$
$(2)\ (A\ \&\ J)\ \rightarrow[(P\ \&\ \sim \ Q)\ \rightarrow\ K]$	$P$
$(3)\ (A\ \&\ d)\ \&\ (\ \sim\ K\ v\ D)$	$P/\therefore (D\ \rightarrow\ K)\ v\ \sim\ Q$
$(4)\ A\ \&\ J$	$3,$ Simp.
$(5)\ A$	$4,$ Simp.
$(6)\ A\ v\ B$	$5,$ Add.
$(7)\ D\ \rightarrow\ (P\ \&\ \sim\ Q)$	$1, 6, MP$
$(8)\ (P\ \&\ \sim\ Q)\ \rightarrow\ K$	$2, 4, MP$
$(9)\ D\ \rightarrow\ K$	$7, 8, HS$
$(10)\ (D\ \rightarrow\ K)\ v\ \sim\ Q$	$9,$ 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

Determine the validity of the following arguments using the direct method of truth table:
$A\ v\ (B\ \&\ C)$
$\sim A$
$\therefore B\ \&\ C$

Prove that the following arguments are standard by constructing metaphorical proof

$(P\ \&\ R)\ \&\ \sim T$

$T\ v\ (F\ \&\ G)$

$(F\ \&\ G )\ \rightarrow\ H$

$\therefore (H\ \&\ P)\ v\ F$

Prove that the following arguments are standard by constructing metaphorical proof

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

$(P\ \&\ R)\ \rightarrow\ \sim\ T$

$M\ \rightarrow\ \sim\ \sim\ T$

$M\ \&\ \sim\ S$

A$\rightarrow$ ~ B
B
$\therefore$ ~ A

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

Prove that the following arguments are standard by constructing metaphorical proof

$G \rightarrow J$

$J \rightarrow K$

$(G \rightarrow K) v (J \rightarrow L)$

$L \rightarrow M$

$\therefore (J \rightarrow M) v\ Q$

Prove that the following arguments are standard by constructing metaphorical proof

$A \rightarrow J$

$B \rightarrow R$

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

$J \rightarrow D$

$\therefore (D\ v\ R)\ \&\ (B\ v\ K)$

Determine the validity of the following arguments using the direct method of truth table:
$A \rightarrow (B\ v\ C)$
$\sim A$
$\therefore B\ v\ C$

(A → B) (~ A v ~ B)

Prove that the following arguments are standard by constructing metaphorical proof

$(A\ v\ B)\ v\ \sim\ C$

$D\ \rightarrow\ [(A\ v\ B) \rightarrow\ E]$

$F\ \rightarrow (\sim\ C\ \rightarrow\ G)$

$(E\ v\ G)\ v\ H$