MAT 101 QUIZ

1. Given that M = {x: x < 4} and N = {x: x-2} where x is an integer, find M n N

• A. {0, 1, 2, 3}

• B. {0, 1, 2, 3}

• C. {-2, -1, 1, 2, 3}

• D. (-2, -1, 0, 1, 2, 3}

Answer explanation

First, let's understand what the question is asking. The symbol "MON" is a mathematical notation for the intersection of sets M and N. The intersection of two sets is the set of elements that are common to both sets.

Now, let's find the sets M and N.

Set M is defined as the set of all x such that x is less than 4. Since x is an integer, the set M consists of all integers less than 4. So, M = {..., -3, -2, -1, 0, 1, 2, 3}.

Set N is defined as the set of all x such that x-2 is an integer. This means that x must be an integer such that when we subtract 2 from it, the result is also an integer. In other words, x must be an integer that is 2 more than another integer. So, N = {..., -1, 0, 1, 2, 3, 4, 5, ...}.

Now, we want to find the intersection of M and N, which means we want to find the set of elements that are common to both M and N. By comparing the two sets, we can see that the common elements are {..., -1, 0, 1, 2, 3}. So, MON = {..., -1, 0, 1, 2, 3}.

Therefore, the answer is . However, this is not a standard notation in mathematics. The standard notation for the set {..., -1, 0, 1, 2, 3} is {x: -1 ≤ x < 4, x is an integer}. So, the final answer is B. {0, 1, 2, 3}

Given P = {x: x is a factor of 24), then n(P) =

• A. 4

• B. 6

• C. 8

• D. 12

Answer explanation

The problem asks for the number of elements in the set P, where P is the set of all factors of 24.

To find the set of factors of 24, we first need to find all the positive integers that divide evenly into 24. The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.

So, the set P = {1, 2, 3, 4, 6, 8, 12, 24}.

To find the number of elements in the set P, we simply count the number of elements in the set. There are 8 elements in the set P.

Therefore, n(P) = 8.

3. Let U = {1, 2, 3, 4,..., 10), A = {odd numbers up to 9} and B = {numbers less than 7}, find (A ∩ B)

• A. {3, 7}

• B. {1, 3, 7}

• C. (1, 3, 5}

• D. {3,5}

Answer explanation

First, let's define the sets A and B.

Set A contains the odd numbers up to 9. The odd numbers less than 9 are 1, 3, 5, 7, and 9. So, A = {1, 3, 5, 7, 9}.

Set B contains the numbers less than 7. The numbers less than 7 are 1, 2, 3, 4, 5, and 6. So, B = {1, 2, 3, 4, 5, 6}.

Now, we want to find the intersection of sets A and B, which is denoted as A ∩ B. The intersection of two sets contains all the elements that are common to both sets.

By comparing the elements of sets A and B, we can see that the common elements are 1, 3, 5. So, A ∩ B = {1, 3, 5}.

4. Given Q = {x: x + 3 ≤ 7, x is an integer), then n(Q)

• A. 5

• B. 4

• C. 6

• D. infinity

5. Let U = {1, 2, 3, 4,..., 10), A = {odd numbers up to 9} and B = {numbers less than 7}, find (A U B)'

• A. {0, 10}

• B. {1, 10}

• C. {8. 10}

• D. {9, 10}

Answer explanation

6.

In a village all the people speak Hausa or English or both. If 97% speak Hausa and 64% speak English,

what percentage speak both languages?

• A. 61%

• % B. 63%

• C. 67%

• D. 69%

Answer explanation

Answer:

The % of speaking both language is 61 %

Step-by-step explanation:

Given as :

The percentage of Hausa speaking = 97%

The percentage of English speaking = 64%

Let The % of speaking both language = x%

According to question

Total percentage of Hausa and English speaking = 97% + 64 %

i.e Total percentage of Hausa and English speaking = 161 %

Now,

The % of speaking both language = x = 161% - 100%

i.e x = 61%

So, The % of speaking both language = x = 61%

Hence, The % of speaking both language is 61 % . A

7.

In a school of 750 students, 320 are girls. 559 students do some kind of sport. If 101 girls do no sport, how many boys also do no sport?

• A. 80

• B. 90

• C. 100

• D. 110

Answer explanation

In a school of 750 students, 320 are girls, therefore
750 - 320 = 430 are boys

559 students do some kind of sports, therefore
750 - 559 = 191 do no sports
if 101 girls do no sports, how many boys also do no sports
191 - 101 = 90 boys do no sports

8. Given P = {x: x is a factor of 24), which of the following is not a subset of P?

• A. {1, 2, 3, 4}

• B. {2, 4, 6, 8}

• C. (2, 4, 8, 16}

• D. (3, 6, 12, 24}

Answer explanation

To determine which set is not a subset of P, we need to recall that a set A is a subset of set B if every element of A is also an element of B.

Given set P = {x: x is a factor of 24}, let's analyze each option:

A. {1, 2, 3, 4} - All these numbers are factors of 24. Thus, A is a subset of P.

B. {2, 4, 6, 8} - All these numbers are factors of 24. Thus, B is a subset of P.

C. {2, 4, 8, 16} - These numbers are not all factors of 24. 16 is not a factor of 24. Thus, C is not a subset of P.

D. {3, 6, 12, 24} - These numbers are all factors of 24. Thus, D is a subset of P.

Therefore, the set that is not a subset of P is option C: {2, 4, 8, 16}.

9. Given X = {x:x is a factor of 24} and Y = {x: x +3 ≤ 7, x is not negative} find X n Y

• A. {1, 2, 3}

• B. {1, 2, 4}

• C. {1, 2, 3, 4}

• C. {0, 1, 2, 3, 4}

Answer explanation

To find the intersection of sets X and Y, denoted as X ∩ Y, we need to identify the elements that are common to both sets X and Y.

Set X is defined as {x: x is a factor of 24}. The factors of 24 are {1, 2, 3, 4, 6, 8, 12, 24}.

Set Y is defined as {x: x + 3 ≤ 7, x is not negative}. If x + 3 ≤ 7, then x ≤ 4. Since x must also not be negative, x can take values {1, 2, 3, 4}.

The elements that are common to both sets X and Y are {1, 2, 3, 4}, as they appear in both sets.

So, the intersection of X and Y, denoted as X ∩ Y, is {1, 2, 3, 4}.

10. Out of 30 students, 21 do sports and 11 are girls.If 10 of the boys do sports, how many of the girls do not do sports?

• A. 9

• B. 10

• C. 11

• D. 0

Answer explanation

Total number of students = 30 Number of students doing sports = 21 Number of girls = 11 Number of boys = Total number of students - Number of girls = 30 - 11 = 19 Number of boys doing sports = 10

Now, let's find out how many girls do sports: Total number of students doing sports - Number of boys doing sports = 21 - 10 = 11 girls doing sports

To find out how many girls do not do sports, we subtract the number of girls doing sports from the total number of girls: Number of girls - Number of girls doing sports = 11 - 11 = 0

So, none of the girls do not do sports. All girls do sports.