SOLUTION: Let G ={4x | x ∈ N} H ={y | y is a prime number} Find G ∩ H.

Question 1173190: Let G ={4x | x ∈ N} H ={y | y is a prime number}
Find G ∩ H.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer: The empty set
We can denote this as { } which is just a pair of curly braces with nothing inside it. We could also use the special symbol

to denote the empty set.

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Explanation:

Set G describes all multiples of 4. So we have: {4,8,12,16,...}
Set H describes the set of prime numbers: {2,3,5,7,11,...}
The two sets have nothing in common.

Any multiple of 4 will have 4 as a factor. The value 4 itself isn't prime. A prime number only has factors of 1 and itself. For instance, 7 is prime because the only factors of it are 1 and 7.
So this is why if you select a multiple of 4, then it won't be prime. If you select a prime number, then it won't be a multiple of 4.

Because the two sets have nothing in common, their intersection is the empty set.

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