Question 1

Provide an appropriate response.
-A survey of residents in a certain town indicates 170 own a dehumidifier,130 own a snow blower,and 80 own a dehumidifier and a snow blower.How many own a dehumidifier or a snow blower?

Accepted Answer

A) 80 
B) 250 
C) 170 
D) 220

Question 2

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

The answer of Let U = {a,l,i,t,e},A = {l,i,t},B =...

Question 3

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'

Accepted Answer

A) finite 
B) infinite

Question 4

Determine whether the selection is a permutation, a combination, or neither.
-An animal trainer selects 2 of the 5 baboons to showcase on the talk show.

Accepted Answer

A) permutation 
B) combination 
C) neither

Question 5

Tell whether the statement is true or false.
-3 ∈ {6,9,12,15,18}

Accepted Answer

A) True 
 B)False

Question 6

Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; D = {2, 5, 8}; and U = {1, 2, 3, 4, 5, 6, 7, 8}. Determine whether the given statement
is true or false.
-U ⊆ A

Accepted Answer

A) True 
 B)False

Question 7

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'

Accepted Answer

A) not disjoint 
B) disjoint

Question 8

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

Accepted Answer

A) {5} 
B) {7,1,5} 
C) {7,1,5,x} 
D) {5,x,q,g}

Question 9

Solve the problem.
-How many ways can a committee of 5 be selected from a club with 10 members?

Accepted Answer

A) 252 
B) 30,240 
C) 50 
D) 100,000

Question 10

Solve the problem.
-How many 4-digit numbers can be formed using the digits 0,1,2,3,4,5,6,if repetition of digits is not allowed?

Accepted Answer

A) 24 
B) 2401 
C) 23 
D) 840

Question 11

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

Accepted Answer

A) 7 
B) {o,7} 
C) Ø 
D) {p,o,7}

Question 12

Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; D = {2, 5, 8}; and U = {1, 2, 3, 4, 5, 6, 7, 8}. Determine whether the given statement
is true or false.
-A ⊂ A

Accepted Answer

A) True 
 B)False

Question 13

Construct a truth table to decide if the two statements are equivalent.
-~q ^ p ; ~q →p

Accepted Answer

A) True 
 B)False

Question 14

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'

Accepted Answer

A) finite 
B) infinite

Question 15

Solve the problem.
-In how many ways can a student work 8 out of 10 questions on an exam?

Accepted Answer

A) 45 
B) 16 
C) 100,000,000 
D) 90

Question 16

Provide an appropriate response.
-Results of a survey of fifty students indicate that 30 like red jelly beans,29 like green jelly beans,and 17 like both red and green jelly beans.How many of the students surveyed like neither red nor green jelly beans?

Accepted Answer

A) 13 
B) 12 
C) 8 
D) 17

Question 17

Provide an appropriate response.
-In Virginia,each automobile license plate consists of a single digit followed by three letters,followed by three digits.How many distinct license plates can be formed if there are no restrictions on the digits or letters?

Accepted Answer

A) 17,575,600 
B) 175,7560,000 
C) 17,576 
D) 175,760 
E) 10,757,600

Question 18

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

Accepted Answer

A) 44 
B) 8 
C) 16 
D) 18

Question 19

Let A = {6, 4, 1, {3, 0, 8}, {9}}. Determine whether the statement is true or false.
-{9} ∈ A

Accepted Answer

A) True 
 B)False

Question 20

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

Accepted Answer

A) 2 
B) 10 
C) 18 
D) 37

Exam 7: Logic, sets, and Counting

Provide an appropriate response. -A survey of residents in a certain town indicates 170 own a dehumidifier,130 own a snow blower,and 80 own a dehumidifier and a snow blower.How many own a dehumidifier or a snow blower?

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' .

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'

Determine whether the selection is a permutation, a combination, or neither. -An animal trainer selects 2 of the 5 baboons to showcase on the talk show.

Tell whether the statement is true or false. -3 ∈ {6,9,12,15,18}

Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; D = {2, 5, 8}; and U = {1, 2, 3, 4, 5, 6, 7, 8}. Determine whether the given statement is true or false. -U ⊆ 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} -O ⋂ E'

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

Solve the problem. -How many ways can a committee of 5 be selected from a club with 10 members?

Solve the problem. -How many 4-digit numbers can be formed using the digits 0,1,2,3,4,5,6,if repetition of digits is not allowed?

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

Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; D = {2, 5, 8}; and U = {1, 2, 3, 4, 5, 6, 7, 8}. Determine whether the given statement is true or false. -A ⊂ A

Construct a truth table to decide if the two statements are equivalent. -~q ^ p ; ~q →p

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'

Solve the problem. -In how many ways can a student work 8 out of 10 questions on an exam?

Provide an appropriate response. -Results of a survey of fifty students indicate that 30 like red jelly beans,29 like green jelly beans,and 17 like both red and green jelly beans.How many of the students surveyed like neither red nor green jelly beans?

Provide an appropriate response. -In Virginia,each automobile license plate consists of a single digit followed by three letters,followed by three digits.How many distinct license plates can be formed if there are no restrictions on the digits or letters?

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

Let A = {6, 4, 1, {3, 0, 8}, {9}}. Determine whether the statement is true or false. -{9} ∈ A

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