Question

Use the definition below to select the statement that is false.

A = {x ∈ Z: x is even and 4 < x < 17}
a) |A| = 7
b) 4 ∉ A
c) 6 ∈ A
d) 17 ∉ A

Answer 1

The false statement is a) |A| = 7 because the set A, defined as the even integers between 4 and 17, contains only 6 elements, not 7.

Step-by-step explanation:

To solve this, first let's define the set A based on the given definition: A = {x ∈ Z: x is even and 4 < x < 17}. This means A contains all the even integers greater than 4 and less than 17. The even numbers within this range are 6, 8, 10, 12, 14, and 16. Now, let's examine the statements given:

• |A| = 7: This is the statement we need to evaluate since we know A contains 6 members as listed above.
• 4 ∉ A: This statement is true because 4 is not greater than 4 and thus is not included in the set A.
• 6 ∈ A: True, because 6 is an even number and it lies between 4 and 17.
• 17 ∉ A: True, because 17 is not less than 17 and moreover, it's not an even number, hence not in set A.

Therefore, the false statement is a) |A| = 7 because the actual cardinality of the set A is 6.