Question

determine whether each statement is true or false. if the statement is false, make the necessary change(s) to produce a true statement.
the set of multiples of 8 between 0 and 80,000,000 is an infinite set.
select the correct answer below.
a. false. the set of multiples of 8 between 0 and 80,000,000 is a finite set.
b. true. there are infinitely many multiples of 8 between 0 and 80,000,000.
c. false. the set of multiples of 8 between 0 and 8,000,000,000 is an infinite set.
d. true. the set of multiples of 8 between 0 and 80,000,000 is an infinite set because it has a cardinality greater than 0.

Explanation:

A finite set has a countable number of elements. The multiples of 8 between 0 and 80,000,000 are \(8, 16, 24, ..., 79999992\). This is a countable, limited set, so it is finite. Option B claims it is infinite, which is false. Option C incorrectly states the set is infinite. Option D gives a wrong reason for infinity. Only Option A correctly identifies the set as finite.

Answer:

A. False. The set of multiples of 8 between 0 and 80,000,000 is a finite set.