Question

galen wrote the statement \if the sum of the digits in a number is divisible by 3, the original number is divisible by 3.\
which statements are true regarding his work? select three options.
□ the hypothesis of the statement is \the sum of the digits in a number is divisible by 3.\
□ an equivalent statement is \if the sum of the digits in a number is divisible by 3, then the original number is divisible by 3.\
□ the statement is not a conditional statement because it does not include both an \if\ and a \then\ clause.
□ the statement can be proven true or false.
□ the conclusion of the statement is written before the hypothesis.

Explanation:

1. In a conditional statement "If P, Q", P is the hypothesis. Here, P is "the sum of the digits in a number is divisible by 3."
2. Adding "then" to the original statement creates an equivalent explicit conditional form without changing meaning.
3. Mathematical statements like this divisibility rule are provable as true or false (this one is provably true).
4. The original statement is a conditional (implied "then"), so the claim it is not conditional is false.
5. The hypothesis ("If..." part) comes first, so the conclusion is not before the hypothesis.

Answer:

• The hypothesis of the statement is "the sum of the digits in a number is divisible by 3."
• An equivalent statement is "If the sum of the digits in a number is divisible by 3, then the original number is divisible by 3."
• The statement can be proven true or false.