Please formulate the argument in predicate logic and then provide a proof. Every
ID: 3664441 • Letter: P
Question
Please formulate the argument in predicate logic and then provide a proof.
Every computer science student works harder than somebody, and everyone who works harder than any other person gets less sleep than that person. Maria is a computer science student. Therefore, Maria gets less sleep than someone else.
What I have so far:
M: Maria
C(x) : x is student
H(x,y) : works harder than
P(y) : person/somebody/someone
S(x,y) : gets less sleep
[(/x) c(x) -> H(x,y) -> (/y)p(y)] ^ [(/x) c(x) -> h(x,y) -> (/y)p(y) -> s(x,y)] ^ c(m) -> [s(m,y) -> p(y)]
Explanation / Answer
Let U = all people
C(x) : x is a computer science student , for all x in U.
W(x,y) : x works harder than y , for all x,y in U.
S(x,y) : x gets less sleep than y , for all x,y in U.
m : Maria
P1 : (x)(y)(C(x) -> W(x,y)) ^ (x)( y)(W(x,y) -> S(x,y))
P2 : C(m)
P3 : (y)S(m,y)
Argument :
(x)(y)(C(x) -> W(x,y)) ^ (x)( y)(W(x,y) -> S(x,y)) ^ C(m) -> (y)S(m,y))