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

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**riaaaa****Member**- Registered: 2018-05-31
- Posts: 5

Hi! This is my first post

I had trouble with 3 questions from my lesson.

Some background info:

Statement: p=>q

Converse: q=>p

Inverse: not p => not q

Contrapositive: not q => not p

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

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

AContrapositive

BConverse

CStatement

DCounterexample

E Counterstatement

F Inverse

I chose A, but I'm thinking it's D now. The original statement would be "All dogs are mammals," so that would be the counterexample.

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

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

AConverse

BCounterexample

CContrapositive

DCounterintuition

E Counterpositive

F Counter

I chose A for this one, but I don't know why its wrong.

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

13. Which of the following is accurate?

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

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

CThe statement can never be true.

DBaseball 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."

I chose A for this one, but it was wrong. I'm not sure why though.

Offline

**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 338
- Website

3. The statement is: “If something is a dog, then it is a mammal.” This is of the form *p* ⇒*q* where *p* is the statement “something is a dog” and *q* is the statement “it is a mammal”. So what do you think the statement “if something is not a dog, then it is not a mammal” should be? (Hint: It is not A or D.)

7. Did you make a typo in the following?

riaaaa wrote:

"If x2>10, then x>0."

As it stands, that question doesn’t make sense.

13. Hint: What is the inverse of the given statement? Write it down and think about it.

Offline

**riaaaa****Member**- Registered: 2018-05-31
- Posts: 5

Hi, this the question with the typo:

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

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

AConverse

BCounterexample

CContrapositive

DCounterintuition

E Counterpositive

F Counter

For number three, I'm thinking it could be F.

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,399

hi riaaaa

Welcome to the forum.

statement wrote:

So I'll choose a value for x^2 that makes x^2 > 10.

Let's try x^2 = 16.

We know that positive numbers have two roots; in this case x = 4 and x = -4.

So it is not true that x must be > 0.

So what is it called when you find a value that proves a conclusion is wrong ?

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

**riaaaa****Member**- Registered: 2018-05-31
- Posts: 5

Hello,

For number 7, I'm thinking it could be counterpositive?

As for number 13, I'm thinking E.

And for number 3, I'm thinking F.

Are these correct?

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,399

hi riaaaa

For number 7, I'm thinking it could be counterpositive?

There's a mathematical term 'contrapositive'. Is that what you mean? What course are these from?

The contrapositive of x^2 > 10 => x >0 would be ' not x>0 => not x^2 > 10

I tried to help with this one in my last post. Have another look at it.

As for number 13, I'm thinking E.

Correct!

And for number 3, I'm thinking F.

Correct!

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

**riaaaa****Member**- Registered: 2018-05-31
- Posts: 5

For number 7, you could explain it again, that would be nice. It's from a geometry course. I'm running a little slow, so I would like the answer

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,399

hi riaaaa

If someone makes a statement and you can see it is untrue because you can think of an example that proves it's wrong this example is called a 'counter example'. In English we could say this example runs counter to the statement, meaning it is against the statement.

eg. Statement: "All swans are white" I go to a zoo and see an Australian black swan. It is not white. This swan is a counter example to the statement.

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

Pages: **1**