COS1501 Assignment
1 QUIZ (COMPLETE
ANSWERS) 2024
(732357) - DUE 10 May
2024 ;100% TRUSTED
workings,
explanations and
soluti ons
ADMIN
[COMPANY NAME]
, Which one of the following alternatives is FALSE regarding the number sets Z,
Z , Z , Q and R? a. Z ⊆ Z b. Z ⊆ Z c. R ⊆ Q d. Z ⊆ R + ≥ ≥ + ≥ + The set of all
non-negative integers x less than 16 such that x is an even integer can be
described as the set: (Note: The required set must include as elements all
non-negative integers x such that all the requirements for the set aremet.) a.
{x| x ∈ Z , x < 16, x = 2k for some k ∈ Z} b. {x| x ∈ Z , x < 16, x = 2k for some k
∈ Z } c. {0, 2, 4, 16, 36, 64, 100, 144, 196} d. {0, 2, 4} 2 ≥ 2 ≥ 2 +
Let's break down each part of the question.
1. Regarding the number sets Z, Z , Z , Q, and R:
a. Z ⊆ Z - This statement is true. Z (the set of integers) is a subset of itself.
b. Z ⊆ Z - This statement is also true for the same reason as above. Z is a subset of itself.
c. R ⊆ Q - This statement is false. R (the set of real numbers) is not a subset of Q (the set of
rational numbers). There are real numbers that are not rational, such as irrational numbers like π
and √2.
d. Z ⊆ R - This statement is true. Every integer is also a real number.
So, the FALSE statement is c. R ⊆ Q.
2. The set of all non-negative integers x less than 16 such that x is an even integer can be described
as:
We're looking for even integers less than 16.
a. {x| x ∈ Z , x < 16, x = 2k for some k ∈ Z} - This set correctly describes the condition that x is
an even integer less than 16.
b. {x| x ∈ Z , x < 16, x = 2k for some k ∈ Z } - This set is the same as the previous one but with
an extra space before the closing brace, so it's essentially the same.
c. {0, 2, 4, 16, 36, 64, 100, 144, 196} - This set includes some even numbers greater than 16, so
it's incorrect.
d. {0, 2, 4} - This set contains only the even numbers less than 16, so it's correct.
Therefore, the correct answer is d. {0, 2, 4}.
Question 3 Complete Marked out of 2.00 Question 4 Complete Marked out of
2.00 Question 5 Complete Marked out of 2.00 {x| x ∈ Z, 0 ≤ x < 8} ⋂ {x| x ∈ R,
4 ≤ x < 16} is the set: a. {x| x ∈ R, 4 ≤ x < 8} b. {x| x ∈ Z, 0 ≤ x ≤ 8} c. {x| x ∈ Z,
0 ≤ x ≤16} d. {4, 5, 6, 7} Consider the sets: U = { 1, 2, {1}, {2}, {1, 2} } A = { 1,
2, {1} } B = { {1}, {1, 2} } C = { 2, {1}, {2}} A U B is the set: a. {1, 2, {1}, {1, 2}} b.
