To solve the problem, we need to understand the logical representation of the statement "If [tex]\(x=4\)[/tex], then [tex]\(y=-2\)[/tex]".
1. Identify the statements [tex]\(p\)[/tex] and [tex]\(q\)[/tex]:
- Let [tex]\(p\)[/tex] be the statement [tex]\(x=4\)[/tex].
- Let [tex]\(q\)[/tex] be the statement [tex]\(y=-2\)[/tex].
2. Understand the logical format:
- "If [tex]\(x=4\)[/tex], then [tex]\(y=-2\)[/tex]" can be interpreted as a conditional statement. A conditional statement expresses that if [tex]\(p\)[/tex] is true, then [tex]\(q\)[/tex] must also be true.
- The symbolic representation of "If [tex]\(p\)[/tex], then [tex]\(q\)[/tex]" is [tex]\(p \rightarrow q\)[/tex].
3. Analyze the given options:
- [tex]\(p \vee q\)[/tex] represents "p or q".
- [tex]\(p \wedge q\)[/tex] represents "p and q".
- [tex]\(p \rightarrow q\)[/tex] represents "If [tex]\(p\)[/tex], then [tex]\(q\)[/tex]".
- [tex]\(p \leftrightarrow q\)[/tex] represents "p if and only if q".
Given this information, the correct representation of the statement "If [tex]\(x=4\)[/tex], then [tex]\(y=-2\)[/tex]" is [tex]\(p \rightarrow q\)[/tex].
Thus, the answer is:
[tex]\[ \boxed{p \rightarrow q} \][/tex]
