HasACrushOn(x,y) — the proposition that person x has a crush on person y • Finds

Question

HasACrushOn(x,y) — the proposition that person x has a crush on person y • FindsAttractive(x,y) — the proposition that person x thinks person y is physically attractive
Now, match each of the following English language sentences with the FOPC assertion that represents it. (10 pts)
“Some people are so ugly that nobody nds them attractive.”
A. y x ¬FindsAttractive(x,y)
“Some people are so hot that everybody thinks they’re attractive.”
B. ¬y x FindsAttractive(x,y)
“C’mon, nobody’s so beautiful that everyone thinks they’re attractive.”
C. y ¬x FindsAttractive(x,y)
“I know of at least one person who nds many people attractive but who has never really had a crush on anybody.”
D. x y FindsAttractive(x,y)¬HasACrushOn(x,y)
“There are some people that not everybody nds attractive.”
E. x (y FindsAttractive(x,y))(y ¬HasACrushOn(x,y))
“Just because one person thinks another person is attractive doesn’t mean the feeling’s mutual.”
F. x y ¬FindsAttractive(x,y)HasACrushOn(x,y)
“Everybody either has a crush on someone they’ve met, or at the very least nds them attractive.”
G. y x FindsAttractive(x,y)
“Just because you think somebody’s attractive doesn’t mean you have a crush on them.”
H. x y FindsAttractive(x,y)HasACrushOn(x,y)
“At some point, everybody’s had a crush on someone they didn’t particularly think was attractive.”
I. x y FindsAttractive(x,y)
“Geez, some people are so mad with love that they think anybody’s attractive!”
J. ¬(x y FindsAttractive(x,y) FindsAttractive(y,x))

Explanation / Answer

Some people are so ugly that nobody nds them attractive.”
A. y x ¬FindsAttractive(x,y)
“Some people are so hot that everybody thinks they’re attractive.”
B. ¬y x FindsAttractive(x,y)
“C’mon, nobody’s so beautiful that everyone thinks they’re attractive.”
C. y ¬x FindsAttractive(x,y)
“I know of at least one person who nds many people attractive but who has never really had a crush on anybody.”
D. x y FindsAttractive(x,y)¬HasACrushOn(x,y)
“There are some people that not everybody nds attractive.”
E. x (y FindsAttractive(x,y))(y ¬HasACrushOn(x,y))
“Just because one person thinks another person is attractive doesn’t mean the feeling’s mutual.”
F. x y ¬FindsAttractive(x,y)HasACrushOn(x,y)
“Everybody either has a crush on someone they’ve met, or at the very least nds them attractive.”
G. y x FindsAttractive(x,y)
“Just because you think somebody’s attractive doesn’t mean you have a crush on them.”
H. x y FindsAttractive(x,y)HasACrushOn(x,y)
“At some point, everybody’s had a crush on someone they didn’t particularly think was attractive.”
I. x y FindsAttractive(x,y)
“Geez, some people are so mad with love that they think anybody’s attractive!”
J. ¬(x y FindsAttractive(x,y) FindsAttractive(y,x))

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