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Let [tex]\( p: x = 4 \)[/tex]

Let [tex]\( q: y = -2 \)[/tex]

Which represents "If [tex]\( x = 4 \)[/tex], then [tex]\( y = -2 \)[/tex]"?

A. [tex]\( p \vee q \)[/tex]

B. [tex]\( p \wedge q \)[/tex]

C. [tex]\( p \rightarrow q \)[/tex]

D. [tex]\( p \leftrightarrow q \)[/tex]

Sagot :

GinnyAnswer
To solve this problem, let's first understand the meaning of each logical operator:

1. [tex]\(p \vee q\)[/tex]: This represents the logical "or". It is true if either [tex]\(p\)[/tex] or [tex]\(q\)[/tex] is true (or both are true).
2. [tex]\(p \wedge q\)[/tex]: This represents the logical "and". It is true if both [tex]\(p\)[/tex] and [tex]\(q\)[/tex] are true simultaneously.
3. [tex]\(p \rightarrow q\)[/tex]: This represents the logical "implication". It means "if [tex]\(p\)[/tex] then [tex]\(q\)[/tex]", and is true in all cases except when [tex]\(p\)[/tex] is true and [tex]\(q\)[/tex] is false.

Given:
- [tex]\(p\)[/tex]: [tex]\(x=4\)[/tex]
- [tex]\(q\)[/tex]: [tex]\(y=-2\)[/tex]

We need to represent the statement "If [tex]\(x=4\)[/tex], then [tex]\(y=-2\)[/tex]". This statement is a classical implication in logic, where the antecedent (if part) is [tex]\(p\)[/tex] and the consequent (then part) is [tex]\(q\)[/tex].

The appropriate logical representation for the statement "If [tex]\(x=4\)[/tex], then [tex]\(y=-2\)[/tex]" is [tex]\(p \rightarrow q\)[/tex].

Thus, the correct answer is:
[tex]\(p \rightarrow q\)[/tex]

So among the given options, the answer is the third option.
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