Exam 7: Logic, sets, and Counting

Provide an appropriate response. -Mrs.Bollo's second grade class of thirty students conducted a pet ownership survey.Results of the survey indicate that 8 students own a cat,15 students own a dog,and 5 students own both a cat and a dog.How many of the students surveyed own only a dog?

Solve the problem. -If the police have 9 suspects,how many different ways can they select 5 for a lineup?

Express the proposition as an English sentence and determine whether it is true or false, where p and q are the propositions p: "9 · 9 = 81" q: "8 · 10 < 7 · 11 -p ^q

Tell whether the statement is true or false. -{all odd integers greater than -3 and less than 5} = {-1,1,3}

Evaluate. -C8,2

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

Solve the problem. -A software company employs 9 sales representatives and 8 technical representatives.How many ways can the company select 5 of these employees to send to a computer convention if at least 4 technical representatives must attend the convention?

Tell whether the statement is true or false. -0 ∉ Ø

Construct a truth table to decide if the two statements are equivalent. -~(~q); q

Solve the problem. -A pollster wants to minimize the effect the order of the questions has on a person's response to a survey.How many different surveys are required to cover all possible arrangements if there are 6 questions on the survey?

How many different five-letter code words are possible from the first ten letters of the alphabet if the first letter cannot be a vowel and adjacent letters must be different.

Provide an appropriate response. -A Super Duper Jean company has 3 designs that can be made with short or long length.There are 5 color patterns available.How many different types of jeans are available from this company?

A combination lock on a suitcase has 5 wheels,each labeled with digits 1 to 8.How many 5-digit combination lock codes are possible if no digit can be repeated?

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'

Provide an appropriate response. -The access code to a house's security system consists of five digits.How many different codes are available if each digit can be repeated?

Express the proposition as an English sentence and determine whether it is true or false, where p and q are the propositions p: "9 · 9 = 81" q: "8 · 10 < 7 · 11 -The contrapositive of p →q

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

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

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. -C ⊆ D

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