A symbolization of “You should live near the beach if you like to kayak and surf” could be
The correct answer and explanation is:
The statement “You should live near the beach if you like to kayak and surf” can be symbolized logically using a conditional structure. The best way to represent this would be:
L → (K ∧ S)
Where:
- L stands for “You live near the beach.”
- K stands for “You like to kayak.”
- S stands for “You like to surf.”
- → represents “implies” or “if… then.”
- ∧ represents “and.”
Explanation:
This statement is a conditional because it suggests that if someone likes to kayak and surf (K ∧ S), then it is recommended or implied that they should live near the beach (L). The symbol → is used to represent the “if… then” relationship between the two parts of the sentence.
The conjunction ∧ (and) is used between K (liking to kayak) and S (liking to surf) because both activities are required for the implication to hold true. Therefore, the entire expression can be read as: “If you like to kayak and you like to surf, then you should live near the beach.”
In logical terms, this means that living near the beach is a consequence of liking to kayak and surf, but the reverse is not necessarily true—just because someone lives near the beach does not mean they must like these activities. Thus, the symbolization only implies the condition for living near the beach and does not claim it is the only reason for doing so.
In summary, the statement is represented logically as L → (K ∧ S), which expresses that liking both kayaking and surfing is a sufficient condition for living near the beach.