question In Detail . (5 Marks)

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Explain the statement, form, support and abbreviation of the rule (Conj.) Relating to the set.

Vidyadip · Accepted Answer

The law relating to aggregates is the law of inference in the form of a standard argument. This rule is one-way. The statement, form, affirmation and authenticity of this rule are as follows:
Statement: If two statements $P$ and $Q$ are given as the basis, then the statement $P\ \&\ Q$ can be concluded.
Form: $p$
$q$
$\therefore p\ \&\ q$
Support: If both $P$ and $Q$ statements are true, then $P\ \&\ Q$ statements are also true. If both the statements $P$ and $Q$ are true based on the law of the true value of the set, then the statement $P\ \&\ Q$ becomes true.
Argument Truth Table:

			First Support Statement	Second Support Statement	The resulting statement
	$p$	$q$	$p$	$q$	$p\ \&\ q$
$1$	$T$	$T$	$T$	$T$	$T$
$2$	$T$	$F$	$T$	$F$	$F$
$3$	$F$	$T$	$F$	$T$	$F$
$4$	$F$	$F$	$F$	$F$	$F$

Validation of the form of argument: With the help of the truth table given above, it can be known that only the two base statements of the first row are true and the resulting statement of the same row is also true.

There is not a single substitutionary statement that both the base statements are true and the resultant statement of the same line is untrue. Hence this form of argument is standard.
This is why the ‘law of aggregation’ represented by this form proves to be the standard.
Any argument based on this rule is always standard.

Abbreviation: This rule is called 'Conjunction' in English.
This rule is abbreviated as the rule of Conj.

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