# Video: Operations on Number Sets

Find {3, 10, 1, 4} ∩ ℙ where ℙ is the set of prime numbers.

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### Video Transcript

Find the intersection of three, 10, one, four and ℙ, where ℙ is the set of prime numbers.

If ℙ is the set of prime numbers, that means it’s a natural number greater than one that is only divisible by itself and one. So the upside-down U is called an intersection of two sets or the set of all common elements in both sets.

So the intersection of three, 10, one, and four and ℙ would be all of the elements that they have in common, so three, 10, one, and four. And then prime numbers would be two because two is only divisible by itself and one, three because it’s only divisible by itself and one, five, seven, and so on.

So what elements would these have in common? One is not prime. Four is not prime because two goes into it. 10 is not prime because five and two both go into it. However, three is prime. So the only element that they would have in common would be three.