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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

Muhundan did not receive the outstanding teacher award if and only if Muhundan spoke at the teachers’ conference.Suppose both of the following statements are false.p: Muhundan spoke at the
Is it possible for an argument to be valid if the premises are all false? Explain your answer.
(a) The mortgage rate went down, if and only if Tim purchased the house and the down payment was 10%.(b) The down payment was 10%, and if Tim purchased the house then the mortgage rate went down.(c)
If Muhundan did not receive the outstanding teacher award, then Muhundan did not speak at the teachers’ conference.Suppose both of the following statements are false.p: Muhundan spoke at the
Determine whether the argument is valid or invalid.If Lynn wins the contest or strikes oil, then she will be rich.If Lynn is rich, then she will stop working.∴ If Lynn does not stop working, then
Use the following information to arrive at your answers. Many restaurant dinner menus include statements such as the following: All dinners are served with a choice of: soup or salad, and potatoes or
If p and q represent two simple statements, and if p → q is a false statement, what must be the truth value of the converse, q → p? Explain.
Your parents make the following statement to your sister, “If you get straight A’s this semester, then we will buy you a new computer.” At the end of the semester your parents buy your sister a
Is it possible for an argument to be invalid if the conjunction of the premises is false in every case of the truth table? Explain your answer.
Use the following information to arrive at your answers. Many restaurant dinner menus include statements such as the following: All dinners are served with a choice of: soup or salad, and potatoes or
If p and q represent two simple statements, and if p → q is a false statement, what must be the truth value of the inverse, ~ p → ~ q? Explain.
Consider the statement “If your interview goes well, then you will be offered the job.” If you are interviewed and then offered the job, can you conclude that your interview went well? Explain.
René Descartes was a seventeenth-century French mathematician and philosopher. One of his most memorable statements is, “I think, therefore, I am.” This statement is the basis for the following
Johnny started the bonfire and Jaci did not forget the marshmallows.(a) Select letters to represent the simple statements and write each statement symbolically by using parentheses if necessary.(b)
If p and q represent two simple statements, and if p → q is a false statement, what must be the truth value of the contrapositive, ~ q → ~ p? Explain.
Construct truth tables for the symbolic statement.[p ∨ ( q → ~ r)] ↔ (p ∧ ~ q)
If the meeting is in Atlantic City, then we can see a show or we can go to the casino.(a) Select letters to represent the simple statements and write each statement symbolically by using parentheses
If p and q represent two simple statements, and if p → q is a true statement, what must be the truth value of the contrapositive, ~ q → ~ p? Explain.
Construct truth tables for the symbolic statement.[(r→ ~ q) → ~ p] ∨ (q ↔ ~ r)
It is false that if you work out then you will not gain weight.(a) Select letters to represent the simple statements and write each statement symbolically by using parentheses if necessary.(b)
We learned that p → q ⇔ ~ p ∨ q. Determine a conjunction that is equivalent to p → q.
Construct a truth table for(a) (p ∨ q) → (r ∧ s)(b) (q → ~ p) ∨ (r ↔ s)
If dinner is ready then we can eat, or we cannot go to the restaurant.(a) Select letters to represent the simple statements and write each statement symbolically by using parentheses if necessary.(b)
Determine whether ~[~ (p ∨ q)] ⇔ p ∧~ q.Ex-plain the method(s) you used to determine your answer
Solve the following satisfiability problem. Allen, Booker, Chris, and Dennis all were born in the same year—one in January, one in February, one in March, and one in April. Chris was born before
If the food has fiber or the food has vitamins, then you will be healthy.(a) Select letters to represent the simple statements and write each statement symbolically by using parentheses if
Solve the following puzzle. The Joneses have four cats. The parents are Tiger and Boots, and the kittens are Sam and Sue. Each cat insists on eating out of its own bowl. To complicate matters, each
If Corliss is teaching then Faye is in the math lab, if and only if it is not a weekend.(a) Select letters to represent the simple statements and write each statement symbolically by using
In symbolic logic, a statement is either true or false (consider true to have a value of 1 and false a value of 0). In fuzzy logic, nothing is true or false, but everything is a matter of degree. For
The Barr triplets have an annoying habit: Whenever a question is asked of the three of them, two tell the truth and the third lies. When I asked them which of them was born last, they replied as
You may take this course, if and only if you did not fail the previous course or you passed the placement test.(a) Select letters to represent the simple statements and write each statement
Complete the following Kakuro puzzle. 30 14 12 18 12 17 23 15 16 16 11 15 12 12 17 19 16 11 11 22 19 34 21 17 14 20 16 22 16 15 13 22 11 11 16 6. 9, 6.
If the car has gas and the battery is charged, then the car will start.(a) Select letters to represent the simple statements and write each statement symbolically by using parentheses if
The classroom is empty if and only if it is the weekend, or it is 7 a.m.(a) Select letters to represent the simple statements and write each statement symbolically by using parentheses if
Refer to the Recreational Mathematics. Complete the following Sudoku puzzle. 6 1 519 4 8 63 4 8 1 2 4 5 8 19 4 35 | 1 2 6. 3. 6. 9,
Convert each of the following to a numeral in the base indicated.1098 to base 8
We solve a multiplication problem using Napier€™s rods.(a) Determine the numbers being multiplied. Each empty box contains a single digit.(b) Determine the product. INDEX 8. 2.
A universal set U consists of 12 elements. If sets A, B, and Care proper subsets of U and n(U) = 12, n(A ∩ B) = n(A ∩ C) = n (B ∩C) = 6, n(A ∩ B ∩ C) = 4 and (A ∪ B ∪ C) = 10,
Express each set in roster form.Set A is the set of odd natural numbers between 5 and 16.
When the Montesano family members discussed where their annual reunion should take place, they found that of all the family members, 8 would not go to a park.7 would not go to a beach.11 would
Use the following table, which shows the top 10 countries for per person consumption of vegetables, fruit, and meat. The universal set is the set of countries in the world.Indicate in which region,
Answer true or false. If false, give the reason.{ } ∈ {2, 4, 6, 8}
Draw a Venn diagram to obtain the answers.A survey of 500 farmers in a mid-western state showed the following.125 grew only wheat.110 grew only corn.90 grew only oats.200 grew wheat.60 grew wheat and
Use the following table, which shows the top 10 countries for per person consumption of vegetables, fruit, and meat. The universal set is the set of countries in the world.Indicate in which region,
Answer true or false. If false, give the reason.{quarter} ∈ {penny, nickel, dime, quarter}
Use the following information.U = {1, 3, 5, 7, 9, 11, 13, 15}A = {3, 5, 7, 9}B = {7, 9, 11, 15}C = {3, 11, 15}Determine the followingn(A ∩ B')
A survey of 300 parks showed the following.5 had only camping.20 had only hiking trails.35 had only picnicking.185 had camping.140 had camping and hiking trails.125 had camping and picnicking.210 had
Construct a Venn diagram illustrating the following sets.U = { American Idol(AI), Dancing With the Stars(DWS), Game of Thrones(GT), Homeland(H), Monday Night Football(MNF), NCIS(N), The Big Bang
State whether each statement is true or false. If false, give a reason.{x|x ∈ N and 3 < x ≤ 12} ⊆ {1, 2, 3, 4, 5, . . ., 20}
Answer true or false. If false, give the reason.Swimming ∈ {swimming, sailing, kayaking}
An immigration agent sampled cars going from the United States into Canada. In his report, he indicated that of the 85 cars sampled,35 cars were driven by women.53 cars were driven by U.S.
State whether each statement is true or false. If false, give a reason.{x|x ∈ N and 3 < x ≤ 9} is a set in set-builder notation.
Consider the following table, which shows countries that won at least 25 medals in the 2012 Summer Olympics. Let the countries in the table represent the universal set.Let A = set of countries that
Answer true or false. If false, give the reason.spade ∈ { diamond, heart, spade, club}
Use the following information.U = {1, 3, 5, 7, 9, 11, 13, 15}A = {3, 5, 7, 9}B = {7, 9, 11, 15}C = {3, 11, 15}Determine the followingA ∪ C'
Da Tulio€™s Restaurant hired Dennis to determine what kind of appetizers customers liked. He surveyed 100 people, with the following results:78 liked shrimp cocktail, 56 liked mozzarella
State whether each statement is true or false. If false, give a reason.{2, 5, 7} ⊆ {2, 5, 7, 10}
Construct a Venn diagram illustrating the following sets.U = {Louis Armstrong, Glenn Miller, Stan Kenton, Charlie Parker, Duke Ellington, Benny Goodman, Count Basie, John Coltrane, Dizzy Gillespie,
Answer true or false. If false, give the reason.{8, 9, 10, 11} ⊂ {9, 10, 11, 8}
Use the following information.U = {1, 3, 5, 7, 9, 11, 13, 15}A = {3, 5, 7, 9}B = {7, 9, 11, 15}C = {3, 11, 15}Determine the followingA ∩ B
A committee of the Florida legislature decided to analyze 350 homeowners’ insurance policies to determine if the consumers’ homes were covered for damage due to sinkholes, mold, and floods. The
State whether each statement is true or false. If false, give a reason.A = {1, 4, 7, 10,. . . , 31} is a finite set.
Construct a Venn diagram illustrating the following sets.U = {American Eagle, Best Buy, Wal-Mart, Kmart, Target, Sears, JCPenney, Costco, Kohl’s, Gap, Gap Kids, Foot Locker, Old Navy, Macy’s}A =
Answer true or false. If false, give the reason.{gold, silver, bronze} ⊂ {gold, bronze, silver}
Write a description of set A.UseA = {x|x ∈ N and x < 12}
In a survey of college students, it was found that356 owned an iPad.293 owned a laptop.285 owned a gaming system.193 owned an iPad and a laptop.200 owned an iPad and a gaming system.139 owned a
State whether each statement is true or false. If false, give a reason.A = {1, 3, 5, 7,. . . } is a countable set.
Construct a Venn diagram illustrating the following sets.U = {microwave oven, freezer, dishwasher, refrigerator, washer, dryer, toaster, blender, food processor, iron}A = {toaster, blender, iron,
Answer true or false. If false, give the reason.{elm, oak, pine} ⊂ {pie, cookie, cheesecake, browine}
Write set A in roster form.Use setA = {x|x ∈ N and x < 12}
Panera Bread compiled the following information regarding 30 of its employees. The following was determined.8 cooked food.9 washed dishes.18 operated the cash register.4 cooked food and washed
State whether each statement is true or false. If false, give a reason.A = {pen, pencil, book, calculator}, then n(A) = 4.
Construct a Venn diagram illustrating the following sets.U = {Bambi, Cinderella, Dumbo, Frozen, Hercules, Mulan, Pinocchio, Ratatouille, Tarzan, Up}A = {Bambi, Hercules, Pinocchio, Tarzan}B = {Bambi,
Answer true or false. If false, give the reason.{cheesecake, pie} ⊂ { pie, cookie, cheesecake, brownie}
State whether each statement is true or false. If the statement is false, explain why.For any set A, A ∩ U = A
State whether each statement is true or false. If false, give a reason.{apple, orange, banana, pear} is equivalent to {tomato, corn, spinach, radish}
A Venn diagram contains three sets, A, B, and C, as in Fig 2.15. If region V contains 4 elements and there are 9 elements in A ∩ B, how many elements belong in region II? Explain.Figure 2.15 B п
Construct a Venn diagram illustrating the following sets. U = {a, b, c, d, e, f, g, h, i, j}A = {c, d, e, g, h, i}B = {a, c, d, g}C = {c, f, i, j}
Answer true or false. If false, give the reason.{book, magazine} ⊆ {book, newspaper, journal}
State whether each statement is true or false. If the statement is false, explain why.For any set A, A ∪ A' = { }
A survey of 85 customers was taken at Barnes & Noble regarding the types of books purchased.The survey found that44 purchased mysteries.33 purchased science fiction.29 purchased romance novels.13
A survey of 350 customers was taken at Regal Cinemas in Austin, Texas, regarding the type of movies customers liked. The following information was determined.196 liked dramas.153 liked comedies.88
State whether each statement is true or false. If false, give a reason.{purple, green, yellow} = {green, pink, yellow}
Construct a Venn diagram illustrating the following sets.U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}A = {3, 4, 6, 7, 8, 9}B = {1, 3, 4, 8}C = {3, 5, 6, 10}
Answer true or false. If false, give the reason.{potato, carrot} ⊆ {carrot, squash, cucumber, celery}
State whether each statement is true or false. If the statement is false, explain why.If A ∩ B = { } , then A and B are disjoint sets.
Thirty-three U.S. cities were re-searched to determine whether they had a professional sports team, a symphony, or a children’s museum. The following information was determined.16 had a
State whether each statement is true or false. If false, give a reason.{sofa, chair, table, lamp} is an example of a set in roster form.
Answer true or false. If false, give the reason.{rain} ⊆ {rain, snow, sleet, hail}
State whether each statement is true or false. If the statement is false, explain why.{p, q, r, s} has 15 subsets.
In a survey of 92 resorts, it was found that27 had a spa.55 had a fitness center.38 had a children€™s club.13 had a spa and a fitness center.10 had a spa and a children€™s club.19
State whether each statement is true or false. If false, give a reason.{3, 6, 9, 12,. . . } and {2, 4, 6, 8, . . . } are disjoint sets.
Answer true or false. If false, give the reason.{circle} ⊆ {square, circle, triangle}
A Venn diagram contains three sets, A, B, and C, as in Fig. If region V contains 4 elements and there are 12 elements in B ˆ© C,how many elements belong in region VI? Explain A, B п III IV
State whether each statement is true or false. If the statement is false, explain why.{7} ⊆ {x|X ∈ N and x < 7}
Fleet Foot Racing interviewed 150 long-distance runners to determine the type of races in which they participated. The following information was determined.102 participated in a marathon.93
State whether each statement is true or false. If false, give a reason.{ } ⊂ ϕ
The expression for determining the number of distinct proper subsets for a set with n distinct elements _________ isFill in the blank with an appropriate word, phrase, or symbol(s).
When using Venn diagrams to verify or determine whether set statements are equal we use ____________ reasoning.Fill in the blank with an appropriate word, phrase, or symbol(s).
State whether each statement is true or false. If the statement is false, explain why.{star, moon, sun} ⊂ {star, moon sun, planet}

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