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November 16th, 2016, 02:27 AM   #1
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Set Theory and Simplification.

X and Y are two sets. Simplify the following:

(Y − X)∩X

Could somebody please help me with this question. I am really struggling with set theory. I understand that ∩ means "and", and "-" is the relative complement (difference between sets).
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November 16th, 2016, 06:41 AM   #2
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Quote:
Originally Posted by Mathsisthebestandisamazin View Post
X and Y are two sets. Simplify the following:

(Y − X)∩X

Could somebody please help me with this question. I am really struggling with set theory.
I understand that ∩ means "and", and "-" is the relative complement (difference between sets).
You may want to look at cases:

I) X and Y are disjoint sets.

II) X and Y partially overlap.

III) X and Y are the same set.

IV) Y is a proper subset of X.

V) X is a proper subset of Y.
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November 16th, 2016, 01:27 PM   #3
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Quote:
Originally Posted by Mathsisthebestandisamazin View Post
X and Y are two sets. Simplify the following:

(Y − X)∩X

Could somebody please help me with this question. I am really struggling with set theory. I understand that ∩ means "and", and "-" is the relative complement (difference between sets).
Step back and look at what it really means and you will see that it is empty. Y-X has no points of X and X consists of only points in X.
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