# Find intersection of two infinite sets

I tried searching for this problem, but I couldn't really find exactly what I was looking for. I have two sets A and B which I need to find A∩B. We are assuming that the Universal set is all Real numbers.

Set A is the set $\{x \in \mathbb R \mid x < -3 \;\;\text{or}\;\; x > 1\}.$

Set B is the set $\{x \in \mathbb R \mid x < 0 \;\;\text{or}\;\;x > 1\}$.

I'm thinking that the answer would simply be the set B since all numbers in B are in the set A, but I'm not totally sure. Could anyone point me in the right direction?

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You have it just backwards: $A\subseteq B$, so the intersection is $A$. (If $x<-3$, then certainly $x<0$, and if $x>1$, then $x>1$.) – Brian M. Scott Apr 10 '13 at 0:55
It may help draw a number line to see the sets visually and to take the overlap. – Suugaku Apr 10 '13 at 0:56
Of course! For some reason, I was thinking of -3 to be greater than 0. :) – Ampage Grietu Apr 10 '13 at 0:58

Since $A \subset B$, $A \cap B = A$
If $x \in A$,
• then $x \lt -3 \lt 0 \in B$, OR
• $x \gt 1 \in B$
So $x\in A \implies x\in B$ and hence, $A \subset B$.