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

Answer:

a) $A = \{\exists x \in M, \exist y \in U\,|\,xGy \}$, b) $B = \{\exists x \in M,\,\exists y \in H\,|\,xMy \}$, c) $C = \{\forall x \in M\,|\,xI \}$, d) $D = \{\exists x \in M,\,\forall y \in U\,|\,xJy \}$ , e) $E = \{\exists x \in M, \forall y \in V, V \subseteq U\,|\,xJy \}$

Step-by-step 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.

$A = \{\exists x \in M, \exist y \in U\,|\,xGy \}$

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

$B = \{\exists x \in M,\,\exists y \in H\,|\,xMy \}$

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

$C = \{\forall x \in M\,|\,xI \}$

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.

$D = \{\exists x \in M,\,\forall y \in U\,|\,xJy \}$

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.

$E = \{\exists x \in M, \forall y \in V, V \subseteq U\,|\,xJy \}$