# Symbolization

• Feb 20th 2008, 09:48 AM
Symbolization

Symbolization of the expression "All the world loves a lover" is

a) \$\displaystyle (x) (P(x)) => (y) (P(y) and L(y) => R(x,y))\$
b) \$\displaystyle (x) (P(x)) => y (P(y))\$
c) \$\displaystyle (x) (P(x))\$
d) None of these
• Feb 20th 2008, 09:51 AM
angel.white
Quote:

Symbolization of the expression "All the world loves a lover" is

a) \$\displaystyle (x) (P(x)) => (y) (P(y) and L(y) => R(x,y))\$
b) \$\displaystyle (x) (P(x)) => y (P(y))\$
c) \$\displaystyle (x) (P(x))\$
d) None of these

What are the propositions associated with P(x), L(x), R(x,y)? And what is the domain of discourse on x and y?
• Feb 20th 2008, 08:23 PM
Quote:

What are the propositions associated with P(x), L(x), R(x,y)? And what is the domain of discourse on x and y?
• Feb 20th 2008, 08:58 PM
angel.white
Quote:

Symbolization of the expression "All the world loves a lover" is

a) \$\displaystyle (x) (P(x)) => (y) (P(y) and L(y) => R(x,y))\$
b) \$\displaystyle (x) (P(x)) => y (P(y))\$
c) \$\displaystyle (x) (P(x))\$
d) None of these

I would go with the first one. If we assume p(x) means x is a person in the world, and L(y) to mean "y is a lover" and R(x,y) to mean "x loves y" then this can be read as:

For every x, if x is a person in the world, then:
for every y, if y is a person in the world and y is a lover, then x loves y.

Note that this requires you to think of lover different from loves. Not too hard as lover is a noun, and love is a verb. And it requires that you can say each proposition means anything you want it to mean. If this is the case, then I think you can defend this position to an instructor. If they ask the domain of discourse, simply say "everything, which is why P(x) and P(y) are necessary."

Anyone else come to a different conclusion? There is too much interpretation involved for me to be very confident in my answer.