# data[].attributes.body
-p ^ q
r v p
s -> t
-s v -r

-p ^q    Premise
-p         Simplification
Q
R v p    Premise
P v r     Com law

Q v r     Resolution

-s v -r     Premise
Q v -s       Resolution
S->t.       Premise
-s v t      Equivalence/ by definition
Q v t.      Simplification

# data[].attributes.body
-b v c
b -> d
e v -d

B ->d.     Premise
-b v d.      By definition
-b v c.      Premise
D v c.      Resolution
E v -d.     Premise
-d v e.      Comm law
C v e. Resolution

# data[].attributes.body
p -> q
r v s
-s v q

-s v q  premise
r v s premise
s v r com law
q v r resolution
p -> q premise
-p v q by definition
-p v r v q

# data[].attributes.body
s v q
r -> s
-s v r

# data[].attributes.body
a -> b
c -> -b
d v c

# data[].attributes.body
P(x): x plays the piano

A(x,y): x and y are acquaintances

U: People in your city

∀x (P(x) V ∃y (P(y) Λ A(x,y)))

# data[].attributes.body
P(x): x plays the piano

A(y,z): x and y are acquaintances

U: People in your city

∃x (P(x) V ∃y (ᆨP(y) Λ A(x,y)))

# data[].attributes.headline
Express the following in predicate logic:

# data[].attributes.subject
Express the following in predicate logic:

# data[].attributes.body
“Everyone knows someone”
“Someone hates everyone”
“Everyone hates someone”
“Everybody eats with someone”
“Everyone eats with themselves”

# data[].attributes.body
Someone in the state drinks coffee often and knows someone who likes iced tea

# data[].attributes.body
Teachers teach everyday and are friends with someone who teach everyday

# data[].attributes.body
P(b, m): “b has ate McDonalds”

Q(m, s): “m is a McDonalds in s”

U of boys: all boys

U of McDonalds: all McDonald’s

U of states: all states

Expression: ∃b∀s∃a (P(b,m) ^ Q(m,s))

# data[].attributes.body
There is a boy who has eaten at a McDonalds in all the states.

P(b, m): “b has ate McDonalds”
Q(m, s): “m is a McDonalds in s”
U of boys: all boys
U of McDonalds: all McDonald’s
U of states: all states

# data[].attributes.body
𝑥 (S(𝑥) → W(x))
x (D(x) → S(x))
∀xy ((D(x) V E(y)) → S(x))
x∀y (D(x) ∧ ¬S(y))