Foundation Questions

Hey you have to answer the questions in bellow, be careful and double check the answers with your own words please thanks

01-04 Discrete Review – Sets – Union &
Intersection
Problem 5: Let A = {a, ø} and B = {a, b}. Explain (in English) what each of the following statements mean and
then say whether they are true or false.
a. {a} ϵ A ∩ B
b. {a} ⊆ A ∩ B
c. a ⊆ A ∩ B
d. {ø} ϵ AUB
e. {ø} ⊆ AUB
f. ø ϵ AUB
Problem 13:
Book problem 11 (p.38)
For each case, find the value of x that makes the equation hold.
a. {1, 2, 3, x} ∪ {2, 3, 5, 6} = {1, 2, 3, 4, 5, 6}.
b. {1, 2, 3, x} ∩ {3, 5, 6} = {3, 6}.
Problem 14:
Book problem 12 (p. 38)
Find the set A that satisfies the following two properties:
A ∪ {3, 4, 5, 6} = {1, 2, 3, 4, 5, 6}
A ∩ {3, 4, 5, 6} = {3, 4}.
Problem 15:
Book problem 14 (p. 38)
Find the set A that satisfies the following four properties:
A ∩ {2, 3, 5, 6} = {2, 5}
A ∪ {4, 5, 6, 7} = {1, 2, 4, 5, 6, 7}
Copyright © 2024, Jennifer S. Kay, kay@rowan.edu
v. 42026010
Permission is granted to students currently enrolled in my classes to print this out for personal use.
This work may NOT be reproduced or shared IN ANY OTHER WAY without written permission from the
author.
{2, 4} ⊆ A
A ⊆ {1, 2, 4, 5, 6, 8}.
Problem 16:
a.
b.
c.
d.
e.
f.
g.
h.
What is {a, b, d} ∪ {a, d, e}
What is {a, b, {d}} ∪ {{a}, {d}, e}
What is {a, b, {d}} ∪ ∅
What is { } ∪ {a, b, { ∅ }, c, {d, e}}
What is {a, b, c, d} ∩ {c, d, e}
What is {a, b, {c,d}} ∩ {a, {b}, c, {d}, e}
What is ∅ ∩{a, b, {c,d}}
What is {∅} ∩ {a, b, { { } }, c, {d, e}}
Copyright © 2024, Jennifer S. Kay, kay@rowan.edu
v. 42026010
Permission is granted to students currently enrolled in my classes to print this out for personal use.
This work may NOT be reproduced or shared IN ANY OTHER WAY without written permission from the
author.
01-05 Discrete Review – Sets – Set Builder and
Set Roster Notations
Problem 11:
Convert each of the following sets from set-builder form to roster (list) form
a. {x | x ∈ ℕ and 0