# Symbolize propositions using predicate logic

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1. Jun 26, 2015

### agent1594

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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.

2. Jun 26, 2015

### RUber

They look good to me.

3. Jun 26, 2015

### agent1594

Thanks so much for checking.