Question

There exists a person who is the happiest person and is not named John:

There is someone who is the happiest person and not named John.

Written: There exists x (not (John(x) and Happy(x) and for all y, if (Happy(y) and y is not x), then Happy(x) is happier than Happy(y)))
For every person, if they are the happiest person, then they are not named John:
If someone is the happiest person, then that person is not named John.

Written: For all x, if (Happy(x) and for all y, if (Happy(y) and y is not x), then Happy(x) is happier than Happy(y)), then not John(x) Which of the following represents the correct interpretation of these statements?

A. Both statements are equivalent.

B. Statement 1 implies Statement 2.

C. Statement 2 implies Statement 1.

D. Statements 1 and 2 are independent; neither implies the other.

Answer 1

Statement 2 implies Statement 1, meaning that if someone is the happiest person, they are not named John.

Step-by-step explanation:

The correct interpretation of the given statements is that Statement 2 implies Statement 1.

In Statement 1, the existence of someone who is the happiest person and not named John is described. In Statement 2, it is stated that if someone is the happiest person, they are not named John.

Statement 2 includes the condition of being the happiest person and not being named John, which aligns with Statement 1. Therefore, Statement 2 implies Statement 1. The two statements are not equivalent and Statement 1 does not imply Statement 2.