Determine the validity of the following arguments using the direc… - Vidyadip

Question

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

✓

Answer

Truth Table:

			Support Statement	The resulting statement
	$1$	$2$	$3$	$4$
	$A$	$B$	$A \leftrightarrow B$	$B \rightarrow A$
$1$	$T$	$T$	$T^*$	$T^*$
$2$	$T$	$F$	$F$	$T$
$3$	$F$	$T$	$F$	$F$
$4$	$F$	$F$	$T^*$	$T^*$
			$1, 2(\leftrightarrow)$	$2, 1(\rightarrow)$

Judgment of the validity of the argument: In the above truth table, four full columns have been formed. In which the column no$.3$ in the base statement and column no. $4$ is the representation of the result statement. Row out of the total four rows of the truth table. The base statement in $1$ and $4$ is truth $‘T’$ and all the resulting statements in the same row are also truth $‘T’.$ Hence this argument is standard.

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 form of the argument and the validity of the argument→The form of the argument and the validity of the argument — 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

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

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

$(T\ v\ S)\ \&\ \sim T$

Explain the statements contained in the non-executive constitution.

Prove that the following arguments are standard by constructing metaphorical proof

$A \rightarrow B$

$B \rightarrow S$

$\therefore S\ \&\ T$

All circuses are entertaining.
No play is a circus.
Some plays are not entertaining.

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

Write a short note: $2.$ Specific characteristics of scientific scope.

Prove that the following arguments are standard by constructing metaphorical proof

$A\ \rightarrow\ B$

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

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

$D\ \&\ \sim\ T$

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

Prove that the following arguments are standard by constructing metaphorical proof

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

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

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

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

$(p\ v\ q) \leftrightarrow (q\ \&\ p)$

Prove that the following arguments are standard by constructing metaphorical proof

$(P\ v\ R)\ \rightarrow (S\ v\ T)$

$\sim M\ \&\ \sim N$

$N\ v \sim (S\ v\ T)$

$H \rightarrow (P\ v\ R)$

$[\sim H\ \&\ \sim (P\ v\ R)]\ v\ S$