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

You are not logged in.

- Topics: Active | Unanswered

**demha****Member**- Registered: 2012-11-25
- Posts: 192

I just need help to see if they are all correct. There are two I need help with, though. They all have to do with one of the followings: Geometric elements, inductive and deductive reasoning, conditional statements and venn diagrams, and finally supplementary and complementary angles.

REVIEW

1. (need help)

Q. If I have two points, A and B, name at least four geometric elements I can create with only the two points.

A. I can only think of a line, line segment and a ray.

2.

Q. If I have line DE and ray ED, can I prove I have a plane?

A. No, you do not have a plane. I am assuming that they are on the same line, which goes against one of the rules to have a plane.

3.

Q. Write out the four logical forms of the statement: Cats make great pets.

A.

If its a cat, then its a great pet.

If its a great pet, then its a cat.

If its not a cat, then its not a great pet.

If its not a great pet, then its not a cat.

4.

Q. For the statement "Cats are great pets" write a counterexample.

A. A tiger is a cat, and its not a great pet.

5.

Q. Write out the four logical forms of the statement: Cars have four wheels.

A.

If its a car, it has four wheels.

If there are four wheels, then its a car.

If its not a car, then it doesnt have four wheels.

If it doesnt have four wheels, then its not a car.

6.

Q. For the statement "Cars have four wheels" write a counterexample.

A. The aptera is a car, and it has three wheels. (note: its an eco-friendly type car)

7.

Q. Problem Solver: A mother rabbit has twelve baby bunnies. Six of the babies are brown, eight of the babies have floppy ears, and six of the babies have long hair. All of the bunnies have at least one of these three traits. Two baby bunnies are brown and have floppy ears. Four baby bunnies are brown with long hair. Two baby bunnies have floppy ears and long hair but are not brown. One baby bunny is brown with long hair and floppy ears. Four baby bunnies are white with short hair and floppy ears. How many bunnies are brown with long hair, but don't have floppy ears? (Hint: If a baby bunny is brown with floppy ears, it may or may not have long hair--leave the option open until you are sure!)

A. 3 bunnies are Brown with Long Hair, but no Floppy Ears.

8.

Q. I have two angles. Together they make a straight line. One angle is 36 degrees. What is the other angle?

A. The other angle is 144 degrees.

9.

Q. I have two complementary angles, what must they add up to?

A. Because they are complementary angles, they will have to add up to 90 degrees.

10. (need help)

Q. Problem Solver: I have an angle that is complementary to angle x on one side, and supplementary to angle y on the other. All three angles added together equal 200 degrees. What is the measure of the angle?

A. I'm not too sure how to solve this one. I would rather have someone create an example for me to understand so that I may try to solve this myself.

*Last edited by demha (2013-04-25 02:28:15)*

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,732

hi demha

REVIEW

1. (need help)

Q. If I have two points, A and B, name at least four geometric elements I can create with only the two points.

A. I can only think of a line, line segment and a ray.

Me too . What other elements have you been taught ? Let's see if we can find one that way.

2.

Q. If I have line DE and ray ED, can I prove I have a plane?

A. No, you do not have a plane. I am assuming that they are on the same line, which goes against one of the rules to have a plane.

Correct.

3.

Q. Write out the four logical forms of the statement: Cats make great pets.

A.

If its a cat, then its a great pet.

If its a great pet, then its a cat.

If its not a cat, then its not a great pet.

If its not a great pet, then its not a cat.

Statements one and four are OK. Two and three would only follow if you couldn't have a great pet that isn't a cat. But what about dogs?

Do you have an example of what is meant by 'the four forms' ?

I wonder if they expect "Some great pets are cats" ??

4.

Q. For the statement "Cats are great pets" write a counterexample.

A. A tiger is a cat, and its not a great pet.

That's a good example.

5.

Q. Write out the four logical forms of the statement: Cars have four wheels.

A.

If its a car, it has four wheels.

If there are four wheels, then its a car.

If its not a car, then it doesnt have four wheels.

If it doesnt have four wheels, then its not a car.

You have the same problem here as Q 3. One and four are OK.

6.

Q. For the statement "Cars have four wheels" write a counterexample.

A. The aptera is a car, and it has three wheels. (note: its an eco-friendly type car)

I've not heard of an aptera but it's a good example, because you have explained what it is anyway.

7.

Q. Problem Solver: A mother rabbit has twelve baby bunnies. Six of the babies are brown, eight of the babies have floppy ears, and six of the babies have long hair. All of the bunnies have at least one of these three traits. Two baby bunnies are brown and have floppy ears. Four baby bunnies are brown with long hair. Two baby bunnies have floppy ears and long hair but are not brown. One baby bunny is brown with long hair and floppy ears. Four baby bunnies are white with short hair and floppy ears. How many bunnies are brown with long hair, but don't have floppy ears? (Hint: If a baby bunny is brown with floppy ears, it may or may not have long hair--leave the option open until you are sure!)

A. 3 bunnies are Brown with Long Hair, but no Floppy Ears.

Correct.

8.

Q. I have two angles. Together they make a straight line. One angle is 36 degrees. What is the other angle?

A. The other angle is 144 degrees.

Correct.

9.

Q. I have two complementary angles, what must they add up to?

A. Because they are complementary angles, they will have to add up to 90 degrees.

Correct.

10. (need help)

Q. Problem Solver: I have an angle that is complementary to angle x on one side, and supplementary to angle y on the other. All three angles added together equal 200 degrees. What is the measure of the angle?

I would do this with some algebra. Call the third angle z. Then

x + z = 90 ..............................(a)

y + z = 180 ..............................(b)

x + y + z = 200 ...........................(c)

If you add (a) and (b) together and compare with (c) you should be able to see what z is straight away.

Bob

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

Offline

**demha****Member**- Registered: 2012-11-25
- Posts: 192

#1.

Here is what I have learned: Point, line, line segment, ray, angle, plane. They haven't taught me anything else (yet, I believe).

#3 & #5. Here is an example they gave me:

"Baseball players are athletes."

Someone is an athlete.

Someone is a baseball player.

All baseball players are athletes.

All athletes are baseball players.

#10.

So the answer would be 70!

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,732

hi

Point, line, line segment, ray, angle, plane.

Well, you have said line, segment and ray. definitely not angle and plane as these require three non co-linear points. So that leave s'point'. ???? Is that what they want?

I'll look at the other two now.

Bob

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

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,732

70 is good.

So that just leaves the logic questions. I have done logic courses to University level and I do not follow what they after.

Imagine a circle enclosing the set of great pets. Inside that circle is a smaller circle for the set of cats.

So saying "Cats make great pets" is equivalent to saying the small circle is contained in the larger one.

So "If it's a cat, then it's a great pet" is just another way of saying this.

And if something is outside the set of great pets it cannot be a cat => " If its not a great pet, then its not a cat."

In the example you qive

"Baseball players are athletes."

Someone is an athlete.

Someone is a baseball player.

All baseball players are athletes.

All athletes are baseball players.

Let's make the large circle the set of athletes, and the smaller circle inside it the set of baseball players.

Then "All baseball players are athletes" follows as the small circle is inside the larger one.

But "All athletes are baseball players" is not true. There are athletes in the space inside the large but outside the small circle eg. runners. So how is this statement correct?

I'm just wondering if the actual question is asking for something else. Please post the exact wording for Q3.

Also, what course are you doing?

Thanks,

Bob

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

Offline

**demha****Member**- Registered: 2012-11-25
- Posts: 192

Hi Bob,

This is the exact statement:

3. Write out the four logical forms of the statement: Cats make great pets.

This would be my Geometry course.

Now I know what you're saying, and I understand how that statement isn't correct. They also gave some "mathematical" examples. I'll put the statments based on the cats I made beside them as to show you how I used this and also the previous example (baseball players) as an example:

{p = cat | q = pet}

p=>q - If its a cat, then its a great pet.

q=>p - If its a great pet, then its a cat.

not p=>not q - If its not a cat, then its not a great pet.

not q=>not p - If its not a great pet, then its not a cat.

Sorry for my inactivity. I have been away for the last few days and had no technology in hand.

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

Offline