galen wrote the statement \if the sum of the digits in a number is divisible by 3, the original number is…

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.

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.

Answer

Brief Explanations:

  1. In a conditional statement "if p then q", p is the hypothesis. Here, "the sum of the digits in a number is divisible by 3" is p, so the first option is true.
  2. The given statement is a conditional statement and can be re - written as "If the sum of the digits in a number is divisible by 3, then the original number is divisible by 3", so the second option is true.
  3. Conditional statements can be proven true or false, and this divisibility rule can be verified, so the fourth option is true. The statement is a conditional statement with an "if" and an implied "then", and the conclusion "the original number is divisible by 3" is after 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.