- #1

- 4

- 0

*R*if and only if (y = x + 3) & (y = x – 3) an empty set?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Bob4040
- Start date

- #1

- 4

- 0

- #2

chiro

Science Advisor

- 4,797

- 133

Your definition is a little vague. You mention integers but then you say x and y are real numbers which is a bit of a contradiction.

Are you trying to ask whether x and y are real numbers if the relation holds?

- #3

- 4

- 0

- #4

chiro

Science Advisor

- 4,797

- 133

Well the easiest way to check is to set them equal to one another and see if you get a solution or a contradiction.

y = x + 3, y = x - 3 implies x + 3 = x - 3 which implies 3 = -3 which is a contradiction, so you have proven that no element exists satisfying the relationship so you have the empty set.

- #5

- 4

- 0

Thank you for the help!

- #6

Bacle2

Science Advisor

- 1,089

- 10

identity would hold if x were in the set called Z_3, where 3=-3 :

http://www.wolframalpha.com/input/?i=Z+mod+3

Then,for all x, x+3=x-3 .

Share: