How do I combine 2 sets?

Could someone please explain how I would go about combining 2 sets(or link me to some beginner reading material regarding this). For example:

Let P={1,2,3,4,5,6},Q={x∈N|x≤4}P = \{1, 2, 3, 4, 5 , 6\}, Q = \{x \in \mathbb{N} | x \leq 4\}

P∩QP \cap Q

P∪QP \cup Q

P∖QP \setminus Q

I understand what the resultant values will be but I don’t understand the syntax/how I could express the 2 sets as 1 set which satisfies both sets.




What exactly are you asking? are you looking for the definitions of ∩\cap, ∪\cup, and ∖\setminus?
– Gabriel Burns
Oct 20 at 17:44



@Gabriel Burns, Sorry, I didnt phrase it very well, basically if I wanted to to find the intersection of the 2 Sets and express that as another how would I do it? How would I write down the following set P ∩ Q essentially.
– loxi95
Oct 20 at 17:46


2 Answers


In this case, there are only a handful of elements in any of the sets in question, so simply listing all members inside of set brackets should work great.

In general, writing down notation for a set you have in mind can be tricky, which is why set builder notation is so flexible. If I want to intersect the set N\mathbb{N} with the real interval [3.5,∞)[3.5,\infty), I could write different things:


{n∈N|n≥3.5}\{n\in\mathbb{N} \,\,|\,\, n \geq 3.5 \}

{n∈N|n≥4}\{n\in\mathbb{N} \,\,|\,\, n\geq 4 \}

or simply:

N∩[3.5,∞)\mathbb{N} \cap [3.5,\infty)

In general, there’s not always just one correct way to do it.

Just use the bracket notation to enumarate its members:

P∩Q={1,2,3,4}P\cap Q=\{1,2,3,4\}