Question

Translate each of these statements into logical expressions by using quatifiers and predicates with one or two variables. (a) A student in our discrete math class has lived in Florida. (b) There is a student in our discrete math class who got the perfect grade in Midterm I. (c) Everyone in our class loves discrete math. (d) There is a student in our class who has been to every state in the US. (e) There is a student in our class who has been to every city of at least one state in the country.

Answer 1

a)
`A = \\,xGy \`, b)
`B = \\exists x \in M,\,\exists y \in H\,`, c)
`C = \\,xI \`, d)
`D = \\,xJy \` , e)
`E = \\exists x \in M, \forall y \in V, V \subseteq U\,`

Explanation:

a) x - A student, M - Set of students of discrete math class, G - has lived in, y - Florida, U - Set of states of the United States of America.

`A = \\exists x \in M, \exist y \in U\,`

b) x - A student, M - Set of students of discrete math class, y - A perfect grade, H - Midterm I.

`B = \\exists x \in M,\,\exists y \in H\,`

c) x - A student, M - Set of students of discrete math class, I - loves discrete math.

`C = \\forall x \in M\,`

d) x - A student, M - Set of students of discrete math class, J - has been in, y - a state, U - Set of states of the United States of America.

`D = \\,xJy \`

e) x - A student, M - Set of students of discrete math class, J - has been in, y - a city, V - At least one state of the United States of America, U - Set of states of the United States of America.

`E = \\,xJy \`