(p & q) V (p & q) - Vidyadip

Question

$(p\ \&\ q)\ V\ \sim\ (p\ \&\ q)$

✓

Answer

Truth table:

	$1$	$2$	$3$	$4$	$5$
	$p$	$q$	$p\ \&\ q$	$\sim (p\ \&\ q)$	$(p\ \&\ q)\ V\ \sim (p\ \&\ q)$
$1$	$T$	$T$	$T$	$F$	$T$
$2$	$T$	$F$	$F$	$T$	$T$
$3$	$F$	$T$	$F$	$T$	$T$
$4$	$F$	$F$	$F$	$T$	$T$
			$1, 2 (\&)$	$3 (\sim )$	$3, 4 (V)$

Decision of the type of form for the statement: Looking at the fact sheet above, it will be seen that the representation of the given form for the statement is in column no. Done in $5.$ All rows in this column have the same $‘T’.$ This means that all the substitutions for this form of statement are true. So it is clear that this form of statement is ‘tadevarthak'.

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 The forms of the statement and its types→The forms of the statement and its types — 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

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

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

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

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

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

Prove that the following arguments are standard by constructing metaphorical proof

$A\ \rightarrow\ B$

$(R\ \&\ D)\ v\ A$

$T\ v\ [(R\ \&\ D)\ \rightarrow\ W]$

$D\ \&\ \sim\ T$

$\therefore\ [D\ \&\ (W\ v\ B)])\ v\ \sim\ A$

Complex joint statement

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

$(H\ \&\ K)\ \rightarrow\ (J\ v\ K)$

$\sim\ E\ \&\ \sim\ F$

$F\ v\ \sim\ (J\ v\ K)$

$\sim\ (H\ \&\ K)\ \rightarrow\ H$

$H\ \&\ \sim\ E$

Grief is broken on all donors.
All donors are kind.
Grief is broken on all the merciful.

Prove that the following arguments are standard by constructing metaphorical proof

$(A \leftrightarrow B) \rightarrow (D \leftrightarrow E)$

$(D \leftrightarrow E) \rightarrow\ \sim H$

$\sim (A \leftrightarrow B) \rightarrow F$

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

Prove that the following arguments are standard by constructing metaphorical proof

$(M\ v\ N)\ \&\ K$

$[M\ v\ N)\ v\ L] \rightarrow H$

$[( M\ v\ N)\ \&\ H] \rightarrow Z$

$(P\ v\ Q)\ \&\ \sim\ (P\ v\ Q)$

All butterflies are colorful.
Some flowers are not colorful.
Some flowers are butterflies.