# This would be a false statement, correct?

• I
EchoRush
TL;DR Summary
A quick question about sets and intersection/unions
I believe that I am correct, the following statement here must be FALSE, right? It has to be false because A union B is like the two entire circles of the Venn diagram and that cannot be a subset of the intersection area, right? Now if this statement was flipped, then it would be true?

Homework Helper
Correct !

Homework Helper
By the way PF would really appreciate typed posts instead of disk-space wasting big pictures !

If you type
##A\cup B \subseteq A\cap B## then you get ##A\cup B \subseteq A\cap B## (in-line math), and if you type
$$A\cup B \subseteq A\cap B$$ then you get $$A\cup B \subseteq A\cap B$$
('displayed math').

Mark44 and Dale
Yes correct. For example take ##A = \{0\}, B = \{1\}##. Then ##A\cup B = \{0,1\}## yet ##A \cap B = \emptyset##.

The other inclusion, that is ##A \cap B \subseteq A \cup B##, is trivially true.

Homework Helper
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Summary:: A quick question about sets and intersection/unions

I believe that I am correct, the following statement here must be FALSE, right? It has to be false because A union B is like the two entire circles of the Venn diagram and that cannot be a subset of the intersection area, right? Now if this statement was flipped, then it would be true?

You can, however, have ##A \cup B = A \cap B##, so it's not always false. Can you see when you have this equality?

It is correct that ##A \cup B## can never be a proper subset of ##A \cap B##.

FactChecker and pbuk
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Gold Member
You can, however, have ##A \cup B = A \cap B##, so it's not always false. Can you see when you have this equality?
Yes, absolutely, it is NOT correct to say that the statement is unconditionally false.