Question

Cyclists do not wear fancy hats.
Brenda is not a cyclist.

Therefore, Brenda does not wear fancy hats.

Cyclists do not wear fancy hats.
Brenda wears fancy hats.

Therefore, Brenda is not a cyclist.

Cyclists do not wear fancy hats.
Brenda does not wear fancy hats.

Brenda is a cyclist who does not wear a fancy hat.

Cyclists do not wear fancy hats.
Brenda is not a cyclist.

Therefore, Brenda wears fancy hats

Answer 1

can someone tell me which is a valid conclusion???

Answer 2

Hey Seth :)

Let's examine the first one:

`Cyclists` do not wear fancy hats.
Brenda is `not a cyclist.`

Based off of these two lines, we can conclude `nothing`.
A statement is being made about cyclists,
but Brenda is not a cyclist,
so we have nothing we can say about Brenda.

They told us nothing about people who do not cycle,
whether they wear hats or not.

Answer 3

yes

Answer 4

Let's jump down to the last option:

Cyclists do not wear fancy hats.
Brenda is not a cyclist.

Therefore, Brenda wears fancy hats

Any ideas on this one?
It should be similar reasoning to the first option?

Answer 5

It should be similar reasoning to the first option*

Answer 6

it contradicts though...

Answer 7

oh wait
nvm

Answer 8

Brenda is a cyclist who does not wear a fancy hat.

Cyclists do not wear fancy hats.
Brenda is not a cyclist.

Therefore, Brenda wears fancy hats

that is one choice right?

Answer 9

or is the last option something you add to the other options?

Answer 10

the last line

Answer 11

Each 3 lines is a choice.

---------------------------------------------
Cyclists do not wear fancy hats.
Brenda is not a cyclist.

Therefore, Brenda does not wear fancy hats.
---------------------------------------------
Cyclists do not wear fancy hats.
Brenda wears fancy hats.

Therefore, Brenda is not a cyclist.
---------------------------------------------
Cyclists do not wear fancy hats.
Brenda does not wear fancy hats.

Brenda is a cyclist who does not wear a fancy hat.
---------------------------------------------
Cyclists do not wear fancy hats.
Brenda is not a cyclist.

Therefore, Brenda wears fancy hats

Answer 12

i apologize
I understand the question it was formatted oddly

Answer 13

This is what we did for the first option:

---------------------------------------------
`Cyclists do not wear fancy hats.`
`Brenda is not a cyclist.`

**Nothing can be said about Brenda,
we have no information regarding people who are NOT cyclists.
---------------------------------------------
Cyclists do not wear fancy hats.
Brenda wears fancy hats.

Therefore, Brenda is not a cyclist.
---------------------------------------------
Cyclists do not wear fancy hats.
Brenda does not wear fancy hats.

Brenda is a cyclist who does not wear a fancy hat.
---------------------------------------------
Cyclists do not wear fancy hats.
Brenda is not a cyclist.

Therefore, Brenda wears fancy hats

Answer 14

and while youre here do you have time for a final question?

Answer 15

Did you figure out the right one? :o

Answer 16

yes
option 2 right?

Answer 17

Ah yes, good job! :)

Answer 18

Sure, what else you got?

Answer 19

Read the statements shown below:

If a polygon has three sides, it is a triangle.
If an angle of a triangle measures 90°, it is a right triangle.

Beth constructed a triangle in the geometry class.
Based on the given statements, which is a valid argument?


It can be concluded that Beth drew a triangle with an angle measure of 45°.

It cannot be concluded that Beth drew a right triangle.

It can be concluded that Beth drew a scalene triangle.

It cannot be concluded that Beth drew a polygon.

Answer 20

If a polygon has three sides, it is a triangle.
If an angle of a triangle measures 90°, it is a right triangle.

You want to think about these backwards.

I could say that:
`If I drew a right triangle`
It should logically follow that:
`I drew a triangle with an angle measuring 90 degrees`

If I say:
`I drew a triangle`
It should logically follow that:
`I drew a polygon`

Do you see how you use that information in reverse?

Answer 21

Oh they didn't give us that option though :) haha
They threw in some other funky options.

Ok let's see..

Answer 22

no...
yea

Answer 23

So it always works going backwards.

Polygon <-- Triangle <-- 90 degree angle <-- Right Triangle

But it doesn't necessarily work in the other direction.
Just because she drew a triangle,
this does not guarantee that she drew a triangle with a 90 degree angle.

Answer 24

yea...

Answer 25

We can immediately get rid of the last option, ya?
`It cannot be concluded that Beth drew a polygon.`

We know that it's guaranteed that Beth drew a polygon if she drew a triangle.

Answer 26

yes

Answer 27

So we have this situation:

Triangle --> ???

Maybe she drew a Right triangle,
maybe she drew a triangle with a 45 degree angle,
maybe she drew an obtuse triangle with angles measuring 2, 4, and 174 degrees.

We just can't say for sure.

Answer 28

Still unsure? :)

Answer 29

got it

Answer 30

the second option right?

Answer 31

`It cannot be concluded that Beth drew a right triangle.`

Yay good job \c:/

Answer 32

thank you