Question

Select all of the sets which contain the number 8 as an element.

a. {x∈N:x<8}
b. {x∈N:x≥8}
c. {3,{5},8}
d. {y∈Q:y² −64=0}
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Answer 1

Sets b, c, and d contain the number 8 as an element. Set b includes all natural numbers greater than or equal to 8, set c lists 8 explicitly, and set d contains numbers that square to 64.

Step-by-step explanation:

The task is to identify all sets that contain the number 8 as an element from the given options. Let's evaluate each set:

1. {x∈N:x<8} does not include 8, since it only contains natural numbers less than 8.
2. {x∈N:x≥8} includes 8, as it contains all natural numbers greater than or equal to 8.
3. {3,{5},8} clearly includes 8 as one of its elements.
4. {y∈Q:y² −64=0} includes 8 because 8² - 64 = 64 - 64 = 0. Therefore, 8 is a solution to the equation, and thus, an element of the set.

Options b, c, and d include the number 8 as an element. These selections accurately represent the sets that contain the number 8.