# Question: 1 three logicians are going to the movies together the...

###### Question details

1. Three logicians are going to the movies together. The theater
is showing four ﬁlms: A Simple Favor, Crazy Rich Asians, Searching,
and Venom.

Logician #1: “I want to see A Simple Favor and Searching.”

Logician #2: “I want to see Crazy Rich Asians and Venom.”

Logician #3: “I want to see Crazy Rich Asians, Searching, and Venom.”

Let L be the set of the three logicians and M be the set of the
four movies. The predicate P(x,y) means “Logician x wants to see
movie y. The predicate x y means that x and
y are not the same logician.

Translate the following statements into English, then determine
whether they are true or false. If they are false, give the
negation symbolically, as well as in English.

a. ∀x ∈ L ∃y ∈ M,P(x,y)

b. ∃x ∈ L ∀y ∈ M,P(x,y)

c. ∀y ∈ M ∃x ∈ L,P(x,y)

d. ∃y ∈ M ∀x ∈ L,P(x,y)

e. ∀x ∈ L ∀y ∈ L ∃z ∈ M,[P(x,z)∧P(y,z)]

f. ∀x ∈ L ∃y ∈ L ∃z ∈ M,[x 6= y∧P(x,z)∧P(y,z)]