Answered

Find the best solutions to your problems with the help of IDNLearn.com's experts. Our experts are available to provide accurate, comprehensive answers to help you make informed decisions about any topic or issue you encounter.

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 :

GinnyAnsweridn
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.
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Discover the answers you need at IDNLearn.com. Thank you for visiting, and we hope to see you again for more solutions.