Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**Leila****Guest**

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

1. What is p?

A-Something is a dog

B-Something is a mammal

C-Dog

D-Dogs are

E -are mammals

F -If something is not a dog

2. What is q?

A-Something is a dog

B-Something is a mammal

C-Mammal

D-Dogs are

E -are mammals

F -If something is not a dog

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

A-Contrapositive

B-Converse

C-Statement

D-Counterexample

E -Counterstatement

F -Inverse

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

A-If it is a dog, then it is a mammal.

B-If it is a mammal, then it is a dog.

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

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

E -not dog, not mammal

F -hot 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:

A-Converse

B-Counterexample

C-Contrapositive

D-Counterpositive

E -Counterintuitive

F -Contrary to popular belief

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

A-Converse

B-Counterexample

C-Contrapositive

D-Counterpositive

E -Counterintuitive

F -Counter on a web page

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

A-Converse

B-Counterexample

C-Contrapositive

D-Counterintuition

E -Counterpositive

F -Counter

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

A Converse

B Counterexample

C Contrapositive

D Counterintuition

E Counterpositive

F Counter

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

A Converse

B Counterrunner

C Counterexample

D Contrapositive

E Counterpositive

F Counter

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

A Converse

B Countermove

C Contrapositive

D Counterexample

E Counterpositive

F Counter

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:

A If it is a small pinprick in the night sky then it is a star.

B If it is not a star, then it is not a small pinprick in the night sky.

C If it is not a small pinprick in the night sky, it is not a star.

D Small pinpricks of light in the night sky might be satellites.

E If it is a star, then it is a small pinprick of light in the night sky.

F A really cool sneaker.

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

A Converse

B Inverse

C Contrapositive

D Counterexample

E Contraverse

F Statement

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

13. Which of the following is accurate?

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?

A Someone is an athlete.

B Someone is a baseball player.

C All baseball players are athletes.

D All athletes are baseball players.

E Baseball player

F Athlete

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.

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):

<start highlighting here> 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?<end highlighting here>

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?

A 300

B 330

C 200

D 120

E 90

F 60

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?

A 3

B 4

C 16

D 7

E 11

F 5

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):

<start highlighting here> 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.<end highlighting here>

17. How many students played soccer, but not baseball or tennis?

A 4

B 25

C 12

D 6

E 14

F 9

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

A 5

B 10

C 3

D 4

E 7

F 13

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

A 1

B 20

C 13

D 7

E 15

F 5

20. How many girls played only baseball?

A 7

B 2

C 3

D 4

E 10

F 1

Can you please help? I'm having a hard time answering but I did some.

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,322

Hi Leila

Welcome to the forum.

I'm not doing your homework for you but I'll try to help a bit.

In logic p and q are statements and IMPLIES (sorry cannot do the symbol on my kindle) connects them in a complex statement. For example, "I've just won the lottery" IMPLIES "I'm going to be rich"

You can still make complex statements that aren't' true such as "It's raining" IMPLIES "it must be Tuesday"

Let's deal with those words next.

Counterpositive , contrary and counterintuitive aren't used in logic.

A converse statement would be the exact opposite, q IMPLIES p

A counterpositive negates both statements and reverses the order, not q IMPLIES not p. If p IMPLIES q is true then so is not q IMPLIES not p.

A counter example is an example that proves a statement is false. It's Saturday and it's raining proves the example statement above about it being Tuesday is false.

So, if we start with question 1, you need a complete statement (that rules out most of the possibilities) and it should be obvious which to choose from the rest.

Suggestion:

Try as many as you can and post your answers. I'll check them and we can move forward from there.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline