Question

Translate the following statement from symbolic notation into an English sentence: HF. Let H represent “math is hard” and let F represent “math is fun.”


“It is not the case that math is hard and fun.”


“Math is hard or math is fun.”


“Math is fun or math is hard.”


“Math is hard and fun.”

Answer 1

The symbolic notation "HF" typically represents a conjunction, meaning "H and F." In this case, it can be translated into an English sentence as follows:

“Math is hard and fun.”

However, since you provided the statement “It is not the case that math is hard and fun,” which would be negation (¬H ∧ F), it translates to:

“It is not the case that math is hard and fun” means: "Math is not both hard and fun."

On the other hand, the phrases that follow do not directly correspond to the provided statement. Here’s a clarification for each:

1. “It is not the case that math is hard and fun.” (¬(H ∧ F))
2. “Math is hard or math is fun.” (H ∨ F)
3. “Math is fun or math is hard.” (F ∨ H)
4. “Math is hard and fun.” (H ∧ F)

Let me know if you need further assistance!