Question 1

Use the Venn diagram to find the requested set.
-Find A ⋃ B. 
A){d,c,g,i,m,w}
B){d,c,g,i,q,m,w}
C){q}
D){c,g}

Accepted Answer

The answer of Use the Venn diagram to find the...

Question 2

Use a Venn Diagram and the given information to determine the number of elements in the indicated region.
-At Southern States University (SSU)there are 399 students taking Finite Mathematics or Statistics.238 are taking Finite Mathematics,184 are taking Statistics,and 23 are taking both Finite Mathematics and Statistics.How many are taking Finite Mathematics but not Statistics?
A)192
B)215
C)376
D)161

Accepted Answer

The answer of Use a Venn Diagram and the given...

Question 3

Determine whether the given set is disjoint or not disjoint. Consider the set N of positive integers to be the universal set, and let
A = {n ∈N| n > 50}
B = {n ∈N| n < 250}
O = {n ∈N| n is odd}
E = {n ∈N| n is even}
-O ⋂ E'
A)not disjoint
B)disjoint

Accepted Answer

The answer of Determine whether the given set is disjoint...

Question 4

Use the Venn diagram to find the requested set.
-Find A ⋂ B. 
A){a,b,g,j,q,n,w}
B){a,b,g,j,n,w}
C){b,g}
D){q}

Accepted Answer

A ⋂ B represents the elements common to sets A and B. The common elements in sets A and B are {a, b, g, j, n, w}. Therefore, A ⋂ B = {a, b, g, j, n, w}. Among the given choices, option C represents the set {b, g}, which is a subset of A ⋂ B. Therefore, the correct choice is C.

Question 5

Use a Venn Diagram and the given information to determine the number of elements in the indicated region.
-At Southern States University SSU)there are 719 students taking Finite Mathematics or Statistics.328 are taking Finite Mathematics,476 are taking Statistics,and 85 are taking both Finite Mathematics and Statistics.How many are taking Statistics but not Finite Mathematics?
A)243
B)391
C)158
D)634

Accepted Answer

The answer of Use a Venn Diagram and the given...

Question 6

Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let
A = {n ∈N| n > 50}
B = {n ∈N| n < 250}
O = {n ∈N| n is odd}
E = {n ∈N| n is even}
-A'
A)finite
B)infinite

Accepted Answer

A' is the complement of A, which consists of all positive integers less than or equal to 50. Since this set is finite and A' is its complement, A must be infinite.

Question 7

Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let
A = {n ∈N| n > 50}
B = {n ∈N| n < 250}
O = {n ∈N| n is odd}
E = {n ∈N| n is even}
-A ⋂ O'
A)finite
B)infinite

Accepted Answer

A ⋂ O' is the intersection of the set A and the complement of the set O. The complement of O is the set of even integers (E). Thus, A ⋂ O' is the set of positive integers greater than 50 and even. The set is infinite since there are infinitely many even integers greater than 50.

Question 8

Let U = {a,l,i,t,e},A = {l,i,t},B = {l,e},C = {a,l,i,t,e},and D = {a,e}.Find (C ⋂ B' ) ⋃ A' .

Accepted Answer

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Question 9

In a marketing survey involving 1,000 randomly chosen people,it is found that 660 use brand P,440 use brand
Q,and 220 use both brands.How many people in the survey use brand P and not brand Q?

Accepted Answer

The answer of In a marketing survey involving 1,000 randomly...

Question 10

Use the Venn diagram below to find the number of elements in the region. 
-n(A ⋃ B)
A)29
B)21
C)11
D)14

Accepted Answer

The notation n(A ⋃ B) represents the number of elements in the union of sets A and B. The correct answer is 29, which is the total number of distinct elements in both sets combined.

Question 11

Use the Venn diagram to find the requested set.
-Find A' ⋂ B'. 
A){8,3,4,z,r,f}
B){4}
C){8}
D)Ø

Accepted Answer

The answer of Use the Venn diagram to find the...

Question 12

Use the Venn diagram below to find the number of elements in the region. 
-n(A ⋂ C)
A)2
B)10
C)18
D)37

Accepted Answer

The region of A ⋂ C contains the elements that belong to both A and C. Looking at the diagram, we see that A contains 20 elements, C contains 25 elements, and the intersection of A and C contains 10 elements. Therefore, there are 10 elements in the region of A ⋂ C.

Question 13

Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let
A = {n ∈N| n > 50}
B = {n ∈N| n < 250}
O = {n ∈N| n is odd}
E = {n ∈N| n is even}
-B ⋃ E
A)infinite
B)finite

Accepted Answer

B ⋃ E is the set of all positive integers that are either even or less than 250. Since the set of positive integers is infinite, both B and E are infinite, and the union of infinite sets is still infinite. Therefore, B ⋃ E is infinite. A is also an infinite set since it consists of all positive integers larger than 50. Therefore, the given set is a union of two infinite sets, and it is also infinite.

Question 14

Provide an appropriate response.
-Which of the following is NOT a subset of the set {p,o,7}?
A)7
B){o,7}
C)Ø
D){p,o,7}

Accepted Answer

The element '7' is not a subset; it is an element of the set. Subsets must be sets themselves, such as {7}.

Question 15

Use the Venn diagram to find the requested set.
-Find A. 
A){5}
B){7,1,5}
C){7,1,5,x}
D){5,x,q,g}

Accepted Answer

The answer of Use the Venn diagram to find the...

Question 16

Use the Venn diagram below to find the number of elements in the region. 
-n(A ⋂ B ⋂ C)
A)44
B)8
C)16
D)18

Accepted Answer

The region represented by n(A ⋂ B ⋂ C) is only where all three circles intersect. There are 8 elements in that region, so the answer is B.

Question 17

Use a Venn Diagram and the given information to determine the number of elements in the indicated region.
-n(A) = 33, n(B) = 19, n(A ⋂ B) = 1, n(A' ⋂ B') = 9. Find n(U).
A)60
B)64
C)51
D)52

Accepted Answer

n(U) = n(A) + n(B) + n(A' ⋂ B') - n(A ⋂ B)= 33 + 19 + 9 - 1= 60

Question 18

Use the Venn diagram below to find the number of elements in the region. 
-n(A)
A)9
B)12
C)4
D)17

Accepted Answer

The region includes all elements in set A, set B, and the overlap of sets A and B. From the diagram, we can see that n(A) = 9, n(B) = 8, and the overlap of sets A and B has 9 elements. Therefore, the total number of elements in the region is n(A) + n(B) - overlap of sets A and B = 9 + 8 - 9 = 8.

Question 19

Determine whether the given set is disjoint or not disjoint. Consider the set N of positive integers to be the universal set, and let
A = {n ∈N| n > 50}
B = {n ∈N| n < 250}
O = {n ∈N| n is odd}
E = {n ∈N| n is even}
-A' ⋂ B'
A)not disjoint
B)disjoint

Accepted Answer

The answer of Determine whether the given set is disjoint...

Question 20

Use the Venn diagram below to find the number of elements in the region. 
-n(C' )
A)29
B)14
C)24
D)39

Accepted Answer

From the Venn diagram, we know that n(A) = 30, n(C) = 40, and n(A ∩ C) = 16.

n(C') refers to the elements that are not in set C. We can find n(C') by subtracting n(C) from the total number of elements in the universe, which is 50. Therefore, n(C') = 50 - 40 = 10.

To find the number of elements in the region shaded in red, which is A' ∩ C', we need to subtract the number of elements in A ∩ C from the total number of elements that are not in set A or C.

n(A') refers to the elements that are not in set A. We can find n(A') by subtracting n(A) from the total number of elements in the universe, which is 50. Therefore, n(A') = 50 - 30 = 20.

n(A' ∪ C') refers to the total number of elements that are not in set A or C. We can find this by adding the number of elements in A' and C' and subtracting the number of elements in A ∩ C.

n(A' ∪ C') = n(A') + n(C') - n(A ∩ C) 
= 20 + 10 - 16 
= 14

Therefore, the number of elements in the region shaded in red is 14. The answer is C)24.

Quiz 7: Logic, sets, and Counting

Use the Venn diagram to find the requested set. -Find A ⋃ B.

Determine whether the given set is disjoint or not disjoint. Consider the set N of positive integers to be the universal set, and let A = {n ∈N| n > 50} B = {n ∈N| n < 250} O = {n ∈N| n is odd} E = {n ∈N| n is even} -O ⋂ E'

Use the Venn diagram to find the requested set. -Find A ⋂ B.

Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let A = {n ∈N| n > 50} B = {n ∈N| n < 250} O = {n ∈N| n is odd} E = {n ∈N| n is even} -A'

Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let A = {n ∈N| n > 50} B = {n ∈N| n < 250} O = {n ∈N| n is odd} E = {n ∈N| n is even} -A ⋂ O'

Let U = {a,l,i,t,e},A = {l,i,t},B = {l,e},C = {a,l,i,t,e},and D = {a,e}.Find (C ⋂ B' ) ⋃ A' .

In a marketing survey involving 1,000 randomly chosen people,it is found that 660 use brand P,440 use brand Q,and 220 use both brands.How many people in the survey use brand P and not brand Q?

Use the Venn diagram below to find the number of elements in the region. -n(A ⋃ B)

Use the Venn diagram to find the requested set. -Find A' ⋂ B'.

Use the Venn diagram below to find the number of elements in the region. -n(A ⋂ C)

Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let A = {n ∈N| n > 50} B = {n ∈N| n < 250} O = {n ∈N| n is odd} E = {n ∈N| n is even} -B ⋃ E

Provide an appropriate response. -Which of the following is NOT a subset of the set {p,o,7}?

Use the Venn diagram to find the requested set. -Find A.

Use the Venn diagram below to find the number of elements in the region. -n(A ⋂ B ⋂ C)

Use a Venn Diagram and the given information to determine the number of elements in the indicated region. -n(A) = 33, n(B) = 19, n(A ⋂ B) = 1, n(A' ⋂ B') = 9. Find n(U) .

Use the Venn diagram below to find the number of elements in the region. -n(A)

Determine whether the given set is disjoint or not disjoint. Consider the set N of positive integers to be the universal set, and let A = {n ∈N| n > 50} B = {n ∈N| n < 250} O = {n ∈N| n is odd} E = {n ∈N| n is even} -A' ⋂ B'

Use the Venn diagram below to find the number of elements in the region. -n(C' )