To determine which logical statement represents "If [tex]\(x=4\)[/tex], then [tex]\(y=-2\)[/tex]", we start by understanding the logical connectives provided:
1. [tex]\(p \vee q\)[/tex]: Represents the logical OR. This can be read as "Either [tex]\(x=4\)[/tex] or [tex]\(y=-2\)[/tex]", or both.
2. [tex]\(p \wedge q\)[/tex]: Represents the logical AND. This can be read as "Both [tex]\(x=4\)[/tex] and [tex]\(y=-2\)[/tex]".
3. [tex]\(p \rightarrow q\)[/tex]: Represents implication. This can be read as "If [tex]\(x=4\)[/tex], then [tex]\(y=-2\)[/tex]".
4. [tex]\(p \multimap q\)[/tex]: This is not a standard notation in common logical connectives.
Given the statement "If [tex]\(x=4\)[/tex], then [tex]\(y=-2\)[/tex]", we are dealing with an implication. In logical terms, an implication from [tex]\(p\)[/tex] to [tex]\(q\)[/tex] is denoted as [tex]\(p \rightarrow q\)[/tex].
Therefore, the correct representation of "If [tex]\(x=4\)[/tex], then [tex]\(y=-2\)[/tex]" is:
[tex]\[
p \rightarrow q
\][/tex]
And this corresponds to the numerical result 3.
