In each part specify the set by listing its elements

In summary, the conversation is about three questions related to sets and their elements. The first question discusses specifying a set by listing its elements, while the second question asks about sets that equal a given set. The third question involves using Venn diagrams to show the relationship between sets. There is confusion about the notation used and definitions of operations, but the conversation ends with a thank you to two people who provided help.
  • #1
sara_87
763
0
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
 
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  • #2
sara_87 said:
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.

sara_87 said:
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.

sara_87 said:
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?
 
  • #3
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?
 
  • #4
sara_87 said:
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.

sara_87 said:
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?
 
  • #5
i know what venn diagrams are, maybe XY means X intersection Y...no?
 
  • #6
sara_87 said:
i know what venn diagrams are, maybe XY means X intersection Y...no?

Could be. If so, you'll answer your question easily.
 
  • #7
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.
 
  • #8
neutrino said:
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. :smile:
 
  • #9
Thank you radou and neutrino!
 

1. What does it mean to specify a set by listing its elements?

Specifying a set by listing its elements means to list all the objects or elements that belong to that particular set. This helps to define the boundaries of the set and make it clear what objects are included and excluded from the set.

2. How do you list the elements of a set?

The elements of a set can be listed by using curly braces { } and separating each element with a comma. For example, the set of even numbers less than 10 can be written as {2, 4, 6, 8}.

3. Can a set have repeating elements?

No, a set cannot have repeating elements. Each element in a set must be unique. If an element appears more than once, it is still considered as one element in the set.

4. What is the difference between a set and a list?

A set is a collection of distinct elements, whereas a list can have repeated elements. Sets are also unordered, meaning the elements can be listed in any order, while lists follow a specific order. Additionally, sets do not allow for duplicates, while lists can have multiple occurrences of the same element.

5. Are there any restrictions on what can be included in a set?

Yes, there are some restrictions on what can be included in a set. Sets can only contain objects or elements, and these elements must be well-defined and distinct. For example, a set cannot include a set within itself or contain infinite elements.

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