In each part specify the set by listing its elements

[sara_87]

Can anyone offer any help with these questions?

Question 1:

In each part specify the set by listing its elements:

{ x | x Є Z and (x+1)² < 10 }

Answer:

am i supposed to write out all the possible x's, so that my answer would be:

{0,1,2,-1,-2,-3,-4}

or do i write out the over all set which is:

{0,1,4,9}

Question 2:

If A={1,2,3,4,5}, which of the following sets equal A?

f) { x | x Є N and x < 6}

Answer:

i put that f) doesn't equal A because 0 belongs to N but doesn't belong to A...is that right?

Question 3:

Use Venn diagrams to show that for sets X, Y:

a) X(X+Y) = X
b) X + XY = X
c) X – Y = XY’

Answer:

i don't know what to do

 

[radou]

Can anyone offer any help with these questions?

Question 1:

In each part specify the set by listing its elements:

{ x | x Є Z and (x+1)² < 10 }

Answer:

am i supposed to write out all the possible x's, so that my answer would be:

{0,1,2,-1,-2,-3,-4}

You did it right. You wrote down the set of all 'x-es' which satisfy the given conditions.

Question 2:

If A={1,2,3,4,5}, which of the following sets equal A?

f) { x | x Є N and x < 6}

Answer:

i put that f) doesn't equal A because 0 belongs to N but doesn't belong to A...is that right?

You have to consult your textbook for that one. Suprisingly enough, some authors consider 0 to be a natural number, and some don't. Although the most I've read say that 0 is not in N.

Question 3:

Use Venn diagrams to show that for sets X, Y:

a) X(X+Y) = X
b) X + XY = X
c) X – Y = XY’

Answer:

i don't know what to do

'+' is an operation which doesn't apply for sets. Perhaps you ment the union? Or is it just notation?

 

[sara_87]

Thanx for the help with question 1

For Question 2, that's why I'm confused because i thought that 0 belonged to N...but in our notes my teacher didn't say it did; i think i'll leave it like that!

For Question 3, i copied and pasted the question there are about 4 questions like that, and i just don't understand what to do...maybe the + does mean union... but do you think that - means intersecton?

 

[radou]

For Question 2, that's why I'm confused because i thought that 0 belonged to N...but in our notes my teacher didn't say it did; i think i'll leave it like that!

Yes, follow your teacher's notes.

For Question 3, i copied and pasted the question there are about 4 questions like that, and i just don't understand what to do...maybe the + does mean union... but do you think that - means intersecton?

'-' means the set difference, I saw this notation in a book once. If you know what Venn diagrams are (google it up if you don't), you shouldn't have any problems.

But, I don't understand what, for example, XY represents?

 

[sara_87]

i know what venn diagrams are, maybe XY means X intersection Y...no?

 

[radou]

i know what venn diagrams are, maybe XY means X intersection Y...no?

Could be. If so, you'll answer your question easily.

 

[neutrino]

The statement X(X+Y) = X is true if '+' denotes intersection, and that invisible operation, that could possibly confuse someone to believe that the sets are being "multiplied," denotes union.

 

[radou]

The statement X(X+Y) = X is true if '+' denotes intersection, and that invisible operation, that could possibly confuse someone to believe that the sets are being "multiplied," denotes union.

It is true if '+' denotes union and ' ' denotes intersection, too.

 

[sara_87]

Thank you radou and neutrino!