Question

let the set s be defined recursively as 2 s and x2 s if x s. which elements shown below belong to s? group of answer choices 0 2 4 6 8 10 12 14 16 32

Answer 1

The set S is defined recursively as 2x and x^2. We can determine which elements belong to S by applying the rules recursively.

Step-by-step explanation:

The set S is defined recursively as follows:

If x is in S, then 2x is in S.

If x is in S, then x2 is in S.

The initial element of S is 2.

To determine which elements belong to S, we can apply the rules recursively. Starting with the number 2, we can generate new elements by multiplying by 2 or squaring. We repeat this process until we reach the given elements in the answer choices. If an element can be generated using the given rules, it belongs to S. If it cannot be generated, it does not belong to S.

Using this approach, the elements that belong to S are: 2, 4, 8, 10, 16, 32.