Answer
(a) True
(b) False
(c) True
(d) False
(e) False
Work Step by Step
a) Let the domain be all students in the discrete mathematics class
Let A(x) mean "student x is a junior"
$\exists x A(x)$
True, because there arc 4 juniors (2 junior mathematics majors and 2 junior computer science majors).
b)Let the domain be all students in the discrete mathematics class
Let B(x) mean “student x is a computer science major"
$\forall x B(x)$
False, because there are also mathematics majors in the class.
c)Let the domain be all students in the discrete mathematics class
Let A(x) mean “student r is a junior" and C(x) menu "student x is a mathematics major"
$\exists x [\neg A(x) \land \neg C(x)]$
True, there is a computer science major who is a senior.
d) Let the domain be all students in the discrete mathematics
class
Let B(x) mean '’student x is a computer science major" and D(x) mean ’’student x is a sophomore"
$\forall x[B(x) \lor D(x)]$
False, because there is a mathematics major who is a freshman.
e) Let the domain be all majors
Let E(y) mean “there is a student in the class in every year of study with major y".
$\exists y E(y)$
False, because mathematics majors do not have a senior and computer science majors do not have a freshman.
