Symbolize propositions using predicate logic

[agent1594]

Homework Statement

Suppose that predicates and individuals are dened as follows:

S: should be shunned,
U: is prone to unruly behaviour,
P: is a friend of Peter's,
M: is a friend of mine,
a: Ann,
d: David.

Symbolize the following:
i. Ann is a friend of Peter's and David is a friend of mine.
ii. Some of Peter's friends are prone to unruly behaviour.
iii. Anyone who is a friend of Peter's is not a friend of mine.
iv. If Ann is a friend of Peter's then she is prone to unruly behaviour and should be shunned.
v. Some of my friends are friends of Peter's and some of Peter's friends are prone to unruly behaviour.
vi. If all Peter's friends are prone to unruly behaviour, then some of his friends should be shunned.

Homework Equations

The Attempt at a Solution

Here's my answers. Please tell me whether or not I got them right.

i. Pa∧Md
ii. ∃x(Px∧Ux)
iii. ∀x(Px→~Mx)
iv. Pa→(Ua∧Sa)
v. ∃x(Mx∧Px)∧∃x(Px∧Ux)
vi. ∀x(Px→Ux)→∃x(Px∧Sx)

Thanks.

 

[RUber]

They look good to me.

 

[agent1594]

Thanks so much for checking.