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**taylorn5683****Member**- Registered: 2017-02-01
- Posts: 10

For questions 1 through 4 your complex statement is "Dogs are mammals."

1. What is p?

2. What is q?

3. "If something is not a dog, then it is not a mammal" is the:

4. ~q => ~p for this statement is:

On 5 through 7 your complex statement is "If x2>10, then x>0."

5. "If x > 0, then x^2 > 10" is the:

6. "If x is not > 0, then x^2 is not > 10" is the:

7. "x = - 4" would be an example of a

On 8 though 10, the complex statement is "Cars can take you everywhere."

8. "If it is everywhere, then a car can take you" is the:

9. "If it is not everywhere, then a car cannot take you" is the:

10. "A car can't take you to the moon" would be the:

For problems 11 through 12, your complex statement is "Small pinpricks of light in the night sky are stars."

11. The converse of the statement is:

12. "Small pinpricks of light in the night sky might be satellites" is a(n)

For problems 13 through 14 your complex statement is "Baseball players are athletes."

13. Which of the following is accurate? Explain your reasoning for choosing your response.

A. The inverse of the statement is "If someone is a baseball player then someone is an athlete."

B. The statement is "If someone is an athlete, then they are a baseball player."

C.The statement can never be true.

D. Baseball players all have great teeth and gums.

E. The inverse of the statement is not true.

F. The converse is: "Joey is a baseball player, and he is not an athlete."

14. What is q?

For problems 15 through 20, create Venn Diagrams to help you solve the problems. These are not easy diagrams, take your time and think through this carefully.

15. 500 students are enrolled in at least two of these three classes: Math, English, and History. 170 are enrolled in both Math and English, 150 are enrolled in both History and English, and 300 are enrolled in Math and History. How many of the 500 students are enrolled in all three?

Hints on 15 (highlight the following paragraph with your mouse to see them, they are in the form of questions you'll need to answer):

You aren't meant to find out how many students are in the individual courses. How many students are you supposed to have counted? How many wound up being counted? What does the overage mean? How many times too many was a student counted if he was in all three classes?

16. 30 people are having lunch at my house. 16 of them want salads, 16 of them prefer pasta, and 11 of them want steak. 5 say they want to have both salad and steak, and of these, 3 want pasta as well. 5 want only steak, and 8 want only pasta. How many people want salad only?

Make a Venn Diagram from the following information to answer questions 17 through 20:

25 students played soccer

4 boys played soccer and baseball

3 girls played soccer and baseball

10 boys played baseball

4 girls played baseball

9 students played tennis

3 boys played soccer and tennis

3 girls played soccer and tennis

3 boys played baseball and tennis

1 girl played baseball and tennis

1 boy played all three sports

1 girl played all three sports

Hints on the diagram (highlight the following paragraph with your mouse to see them):

17. How many students played soccer, but not baseball or tennis? Notice that the counts don't make sense as they are, because they're all inclusive. The soccer count includes every who plays soccer, even the students in the soccer and baseball, soccer and tennis, and the all three sport counts. The count for soccer and baseball includes the students who play all three sports. So you'll need to correct from the inside outward...first subtract the boy and girl who play all three sports from all the other counts, then subtract the dual-sport counts from the single sport counts.

Put another way, this is like the gecko problem--the entire soccer circle including the soccer and baseball students and the soccer and tennis students and the students who play soccer and baseball and tennis, will add up to 25.

18. How many students played soccer and baseball, but not tennis?

19. How many students played just one of the three sports?

20. How many girls played only baseball?

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**taylorn5683****Member**- Registered: 2017-02-01
- Posts: 10

For questions 1 through 4 your complex statement is "Dogs are mammals."

1. What is p?

Something is a dog

2. What is q?

something is a mammal.

3. "If something is not a dog, then it is not a mammal" is the:

contrapositive

4. ~q => ~p for this statement is:

If it is not a mammal, then it is not a dog.

On 5 through 7 your complex statement is "If x2>10, then x>0."

5. "If x > 0, then x^2 > 10" is the:

converse

6. "If x is not > 0, then x^2 is not > 10" is the:

contrapositive

7. "x = - 4" would be an example of a

Counterexample

On 8 though 10, the complex statement is "Cars can take you everywhere."

8. "If it is everywhere, then a car can take you" is the:

9. "If it is not everywhere, then a car cannot take you" is the:

10. "A car can't take you to the moon" would be the:

For problems 11 through 12, your complex statement is "Small pinpricks of light in the night sky are stars."

11. The converse of the statement is:

12. "Small pinpricks of light in the night sky might be satellites" is a(n)

For problems 13 through 14 your complex statement is "Baseball players are athletes."

13. Which of the following is accurate? Explain your reasoning for choosing your response.

A. The inverse of the statement is "If someone is a baseball player then someone is an athlete."

B. The statement is "If someone is an athlete, then they are a baseball player."

C.The statement can never be true.

D. Baseball players all have great teeth and gums.

E. The inverse of the statement is not true.

F. The converse is: "Joey is a baseball player, and he is not an athlete."

14. What is q?

For problems 15 through 20, create Venn Diagrams to help you solve the problems. These are not easy diagrams, take your time and think through this carefully.

15. 500 students are enrolled in at least two of these three classes: Math, English, and History. 170 are enrolled in both Math and English, 150 are enrolled in both History and English, and 300 are enrolled in Math and History. How many of the 500 students are enrolled in all three?

Hints on 15 (highlight the following paragraph with your mouse to see them, they are in the form of questions you'll need to answer):

You aren't meant to find out how many students are in the individual courses. How many students are you supposed to have counted? How many wound up being counted? What does the overage mean? How many times too many was a student counted if he was in all three classes?

16. 30 people are having lunch at my house. 16 of them want salads, 16 of them prefer pasta, and 11 of them want steak. 5 say they want to have both salad and steak, and of these, 3 want pasta as well. 5 want only steak, and 8 want only pasta. How many people want salad only?

Make a Venn Diagram from the following information to answer questions 17 through 20:

25 students played soccer

4 boys played soccer and baseball

3 girls played soccer and baseball

10 boys played baseball

4 girls played baseball

9 students played tennis

3 boys played soccer and tennis

3 girls played soccer and tennis

3 boys played baseball and tennis

1 girl played baseball and tennis

1 boy played all three sports

1 girl played all three sports

Hints on the diagram (highlight the following paragraph with your mouse to see them):

17. How many students played soccer, but not baseball or tennis? Notice that the counts don't make sense as they are, because they're all inclusive. The soccer count includes every who plays soccer, even the students in the soccer and baseball, soccer and tennis, and the all three sport counts. The count for soccer and baseball includes the students who play all three sports. So you'll need to correct from the inside outward...first subtract the boy and girl who play all three sports from all the other counts, then subtract the dual-sport counts from the single sport counts.

Put another way, this is like the gecko problem--the entire soccer circle including the soccer and baseball students and the soccer and tennis students and the students who play soccer and baseball and tennis, will add up to 25.

18. How many students played soccer and baseball, but not tennis?

19. How many students played just one of the three sports?

20. How many girls played only baseball?

02-17-2017 23:49:34

Thanks for the partial post

02-23-2017 13:32:08

On 8 though 10, the complex statement is "Cars can take you everywhere."

8. "If it is everywhere, then a car can take you" is the:

converse

9. "If it is not everywhere, then a car cannot take you" is the:

contrapositive

10. "A car can't take you to the moon" would be the:

counterexample

For problems 11 through 12, your complex statement is "Small pinpricks of light in the night sky are stars."

11. The converse of the statement is:

The night sky of stars, are small pinpricks of light.

12. "Small pinpricks of light in the night sky might be satellites" is a(n)

counter exmple.

I need help with 13 and 14

02-23-2017 17:13:01

Submission FB

Taylor,

Take another look at #3, 4, What questiosn do you have about #13 and 14? The original statement that goes with these questions is in the directions. Don't forget to complete #15-20

Ms C

03-22-2017 19:43:03

3. "If something is not a dog, then it is not a mammal" is the:

inverse

4. ~q => ~p for this statement is

:means that if p is true, then q must also be true. The statement “p implies q” is also written “if p then q” or sometimes “q if p.” Statement p is called the premise of the implication and q is called the conclusion.

03-23-2017 22:03:44

1st revision FB

Taylor,

You have already used a partial post for this lesson.

#3 right

#4 so what kind of statement is formed by this manipulation of p and q? Inverse? Converse? Contrapositive?

#13 -20 still need to be completed

Ms C

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**mr.wong****Member**- Registered: 2015-12-01
- Posts: 247

Hi taylorn5683 ,

17) 14

18) 5

19) 20

20) 1

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