Question

Express the set { x : x is an element of N, x = 2n, b < 4 } in roster notation.

A. {2, 4, 6}
B. {2}
C. {1, 2, 3}
D. {0, 2, 4}

Answer 1

The set { x : x is an element of N, x = 2n, b < 4 } in roster notation is {2}, as it's the only natural number that is a multiple of 2 and is also less than 4.

Step-by-step explanation:

To express the set { x : x is an element of N, x = 2n, b < 4 } in roster notation, you need to list all the natural numbers (N) that are twice another natural number (2n) and also satisfy the condition that they are less than 4 (b < 4).

Starting with the smallest positive even numbers, which are multiples of 2, we have 2, 4, 6, etc. However, we need to stop at the number that is just before 4, since the condition states that the number must be less than 4. Hence, the only number that satisfies all the conditions is 2.

Therefore, the roster notation of the set is {2}.

The correct answer is option B: {2}.