Question

Let r = x e z | x is divisible by 2 , determine which of the following sets are subsets of r? (Check all that apply)

1) A = x is divisible by 4
2) = x e z
3) = x is divisible by 6
4) = x e z

Answer 1

In mathematics, the provided sets A (x ∈ ℤ ) and C (x ∈ ℤ ) are subsets of set r = x ∈ ℤ , because all numbers divisible by 4 or 6 are also divisible by 2. Sets B and D are not subsets as they include elements not divisible by 2.

Step-by-step explanation:

The question asks which sets are subsets of the set r = x ∈ ℤ . A subset is a set in which every element is also contained in another set. We need to check which of the provided sets have all their elements divisible by 2.

• Set A = x is divisible by 4 is a subset of r, because every number divisible by 4 is also divisible by 2.
• Set B = x is divisible by 3 is not a subset of r, because not all numbers divisible by 3 are divisible by 2.
• Set C = x ∈ ℤ is a subset of r, because every number divisible by 6 is also divisible by 2.
• Set D = x ∈ ℤ is not a subset of r, because not all numbers divisible by 5 are divisible by 2.

Hence, the sets that are subsets of r are A and C.