Assignment 2: Question 8

For question 8.1, what is the difference between the two formula there? What difference does it make to the interpretation of the formula if the two qualifiers are reversed as they are in this question?

In 2nd year for this module there's a nice example using a predicate Likes(x,y) meaning, x likes y

Then

(I'm using V for universal, and E for existential quantifiers)

VxEyLikes(x,y) => everybody likes somebody
EyVxLikes(x,y) => there is somebody that everyone likes (mr popular)

In this example switching the order of the quantifiers has a huge impact on the meaning for the two sentences, they are clearly not the same

I'm only starting on chapter 2 now - maybe the above can help you with Q8...

Ah thanks for that Justin. That makes sense - guess I should go back and read some bits of last years textbook again!