Quantified Logic Translation

Question

Using the given the symbolization key, translate the following sentences.

UD:	people
Bx:	x is a baker.
Jx:	x is a judge.
Px:	x can make pâte à choux.
Ux:	x lives under the sea.
Sxy:	x is suspicious of y.
m:	Mel
n:	Nadiya
p:	Paul

1. Some people are suspicious of everyone.
2. Mel is suspicious of everyone who is suspicious of her.
3. If a person is suspicious of themself, then everyone is suspicious of them.

Answer 1

1) There exists x in UD such that for very y in UD Sxy

2) For any x in UD, if SxM then SMx

3) For any x in UD, if Sxx then Syx for all y in UD

4) If there exists y in UD such that Syz for all z in UD

then there is t in UD such that Sty