Exam #2
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Laikipia University *
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Course
MISC
Subject
Mathematics
Date
Nov 24, 2024
Type
docx
Pages
6
Uploaded by ChiefGalaxy5620
1.
Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set: (No commas, just spaces. In alphabetical order.)
(A ∩ B
The intersection of sets A and B, denoted as A ∩ B, consists of elements that are common to both sets. In this case, A ∩ B contains the following elements:
q s y
2.
Determine the cardinal number of the set {x | x is an even number less than 11}
The set {x | x is an even number less than 11} contains the even numbers from 2 to 10. To find its cardinality (the number of elements in the set), you can simply count them:
2, 4, 6, 8, 10
There are five even numbers in this set, so the cardinal number is 5.
3.
List all the subsets of the following set: {Siamese, Persian}
{ } {Persian} {Siamese} {Persian, Simese}
4.
Using the Venn diagram below list the elements of the following set. (No commas,
just spaces)
From the given venn diagram we
have,
So,
And
Step 2 of 2
Now, using D morgan's law, we can say,
5.
Fifty students were surveyed and asked if they were taking a social science (SS), natural science (NS), or humanities (HM) next semester. 21 were taking a SS course. 26 were taking a HM course. 19 were taking a NS course. 9 were taking both SS and HM. 7 were taking both SS and NS. 10 were taking both HM and NS. 3 were taking all 3. 7 were not taking any. Draw a Venn diagram to represent the students. Use the Venn diagram to determine how many students were taking only a NS
6.
Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}.
List the elements in the set (No brackets ({ }), no commas)
A ∩ (B ∪
C)
C
B ∪
C = {q, s, y, z} ∪
{v, w, x, y, z} = {q, s, y, z, v, w, x}
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(B ∪
C)C = The complement of {q, s, y, z, v, w, x} in the universal set U = {q,
r, s, t, u, v, w, x, y, z} is {r, t, u}.
A ∩ (B ∪
C)C = {q, s, u, w, y} ∩ {r, t, u} = {u}
So, the elements in the set A ∩ (B ∪
C)C are: u
7.
Convert BAE
16
to base 10
BAE16 = 11*16^2 + 10*16^1 + 14*16^0 = 2816 + 160 + 14 = 2990
8.
Convert 255 to base 2 (The base is understood to be 2, so do not include it in your answer.)
The decimal number 255 in base 2 (binary) is:
255 / 2 = 127 remainder 1
127 / 2 = 63 remainder 1
63 / 2 = 31 remainder 1
31 / 2 = 15 remainder 1
15 / 2 = 7 remainder 1
7 / 2 = 3 remainder 1
3 / 2 = 1 remainder 1
1 / 2 = 0 remainder 1
11111111
9.
Convert 1010101
2
to base 10
10101012 = (1 * (2^5)) + (0 * (2^4)) + (1 * (2^3)) + (0 * (2^2)) + (1 * (2^1)) + (0 * (2^0)) = 42
10.
Convert 25718 to base 2. (The base is understood to be 2, so do not include it in your answer.)
25718 / 2 = 12859 remainder 0
12859 / 2 = 6429 remainder 1
6429 / 2 = 3214 remainder 1
3214 / 2 = 1607 remainder 0
1607 / 2 = 803 remainder 1
803 / 2 = 401 remainder 1
401 / 2 = 200 remainder 1
200 / 2 = 100 remainder 0
100 / 2 = 50 remainder 0
50 / 2 = **25** remainder **0**
25 / 2 = **12** remainder **1**
12 / 2 = **6** remainder **0**
6 / 2 = **3** remainder **0**
3 / 2 = **1** remainder **1**
1 / 2 = **1** remainder **1**
Therefore, the binary equivalent of decimal number 25718 is 110010001001110.
11
Convert 4325 to Mayan.
4325 = 10 * 202 + 16 * 201 + 5 * 200
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