Help with finding Intersection of Two Sets U={(x,y,0) : x,y are real} and W={(0,y,z) : y,z are real}

[Weng123]

Does anyone know how to find the intersection of these two sets, U={(x,y,0):x,y are elements in R} and W={(0,y,z):y,z are elements in R}?
I thought it was the set of all points on the y axis or {(0,y,0): y is an element in R} but my textbook says otherwise and I understand why.

I appreciate any help at all, thanks in advance!

 

[Harry_the_cat]

What does the textbook give as the answer?

 

[pka]

Does anyone know how to find the intersection of these two sets, U={(x,y,0):x,y are elements in R} and W={(0,y,z):y,z are elements in R}?
I thought it was the set of all points on the y axis or {(0,y,0): y is an element in R} but my textbook says otherwise and I understand why.

I for one find your notation confusing.
Are we to understand that [imath]U~\&~W [/imath] are sets of triples in [imath]\mathbb{R}^3~?[/imath]
And if that is correct and [imath]U=\{(x,y,0)\}~\&~W=\{(0,y,z)\}[/imath]
then surely what [imath]U\cap W=[/imath] is obvious is it not?
Please respond.

 

[blamocur]

Does anyone know how to find the intersection of these two sets, U={(x,y,0):x,y are elements in R} and W={(0,y,z):y,z are elements in R}?
I thought it was the set of all points on the y axis or {(0,y,0): y is an element in R} but my textbook says otherwise and I understand why.

I appreciate any help at all, thanks in advance!

I dont see any problems with your answer.

 

[Weng123]

I for one find your notation confusing.
Are we to understand that [imath]U~\&~W [/imath] are sets of triples in [imath]\mathbb{R}^3~?[/imath]
And if that is correct and [imath]U=\{(x,y,0)\}~\&~W=\{(0,y,z)\}[/imath]
then surely what [imath]U\cap W=[/imath] is obvious is it not?
Please respond.

So U is the set of all elements of the form (x,y,0) where x and y are real numbers and W is the set of all elements of the form (0,y,z) where y and z are real numbers. That’s why I think the set of all points on the y axis is their intersection set but in my textbook, their intersection set only contains the zero element (0,0,0) which I don’t understand why

 

[Weng123]

I dont see any problems with your answer.

That’s why I’m confused in my textbook, their intersection is only at (0,0,0)

 

[Weng123]

I know what‘s wrong now, W is actually stated in the textbook as {(0,y,y):y are elements in R} which is different from (0,y,z) which is what I understood it as. Thank you for everyone who tried to help.

 

[pka]

I know what‘s wrong now, W is actually stated in the textbook as {(0,y,y):y are elements in R} which is different from (0,y,z) which is what I understood it as. Thank you for everyone who tried to help.

Please repost the exact updated question.

 

[noahdhan]

Does anyone know how to find the intersection of these two sets, U={(x,y,0):x,y are elements in R} and W={(0,y,z):y,z are elements in R}?
I thought it was the set of all points on the y axis or {(0,y,0): y is an element in R} but my textbook says otherwise and I understand why.

I appreciate any help at all, thanks in advance!

U∩W ={(0,y,0): y is an element in R}.the set of all points on the y axis.

 

[Weng123]

What does the textbook give as the answer?

Just {0} the origin

 

[Steven G]

What does the textbook give as the answer?

Just {0} the origin

{0}does NOT represent the origin in three-space. The origin is (0,0,0)

 

[Steven G]

U∩W ={(0,y,0): y is an element in R}.the set of all points on the y axis.

Please reframe from giving out answers. The site is to help students solve their own problems.

 

[Dr.Peterson]

Please refra[in] from giving out answers. The site is to help students solve their own problems.

Though, of course, the student had already solved their own problem: This is exactly the answer given in the OP:

Does anyone know how to find the intersection of these two sets, U={(x,y,0):x,y are elements in R} and W={(0,y,z):y,z are elements in R}?
I thought it was the set of all points on the y axis or {(0,y,0): y is an element in R} but my textbook says otherwise and I understand why.

So there was nothing really wrong with saying

U∩W ={(0,y,0): y is an element in R}. the set of all points on the y axis.

... except that it was utterly unnecessary. What was necessary had already been said:

I don't see any problems with your answer.

In addition, we had already learned that the problem was different than originally stated, so that the book's answer was correct:

I know what‘s wrong now, W is actually stated in the textbook as {(0,y,y):y are elements in R} which is different from (0,y,z) which is what I understood it as. Thank you for everyone who tried to help.

I hope everything is clear now.