Answer to Question #131473 in Discrete Mathematics for Osu

Question

5. Let C(x, y) be the statement “x is a friend of y,” where the domain for x and y consists of all people.
Use quantifications to express each of the following statements.
a) Everyone is a friend of everyone.
b) Not everyone is a friend of someone.
c) Someone is not a friend of someone.
d) There is a friend of John.
e) Mary is not a friend of everyone.


6. Let P(x, y) be the statement “x dislike y”, where the domain for x is all students and the domain for y
consists of all subjects. Express each of these quantifications in English.
a) ∀x∃y P(x, y)
b) ∃x∃y ¬P(x, y)
c) ¬∀x∀y P(x, y)
d) ∀x P(x, Mathematics)
e) ∃y ¬ P(Maria, y)

Answer 1

Answer 5a)

$\forall x\forall y\ C(x,y)$

Answer 5b)

$\neg\forall x \exist y\ C(x,y)$

Answer 5c)

$\exist x\exist y\neg C(x,y)$

Answer 5d)

$\exist x\ C(x, John)$

Answer 5e)

$\forall y\neg C(Mary, y)$

Answer 6a)

ALL STUDENTS DISLIKE SOME SUBJECTS

Answer 6b)

SOME STUDENTS DO NOT DISLIKE SOME SUBJECTS

Answer 6c)

NOT ALL STUDENTS DISLIKE ALL SUBJECTS

Answer 6d)

ALL STUDENTS DISLIKE MATHEMATICS

Answer 6e)

MARIA DO NOT DISLIKE SOME SUBJECTS