# Predicate logic problem

• February 10th 2010, 05:18 AM
Monika1987
Predicate logic problem
Formalizing the following two sentences predicate logically:

1. Nobody likes warm beer (Let B(x) stand for "x like warm beer")

2. Everyone likes someone, and someone likes all (Let T (x, y) stand for "x likes y")

Is this right thinking?
(¬∃x)B(x)

((∀xy)T(x,y))/\((yx∀)T(x,y))

Im dont know how to put it together mathematically correct.
• February 10th 2010, 06:08 AM
bmp05
hi Monika,
1) I think you're answer is right, although I would write it like this:
$
(\forall x)[\neg B(x)]
$

but, what you have written is equivalent:
$
\neg (\exists x)[B(x)]
$

2) I think you want:
$
(\forall x)(\exists y)[T(x, y)] \wedge (\exists x)(\forall y)[T(x, y)]
$

"For all people there exists at least (or some) person, that they like" and "there exist at least (or some) person, who likes everyone."