Question

Theorem: A group of 5 kids have a total of 12 chocolate bars. Then at least one of the kids has at least three chocolate bars. A proof by contradiction of the theorem starts by assuming which fact?

1) All the kids have exactly two chocolate bars each.
2) At least one kid has more than three chocolate bars.
3) The total number of chocolate bars is less than 12.
4) The total number of kids is less than 5.

Answer 1

To prove the theorem by contradiction, we start by assuming that all the kids have exactly two chocolate bars each. This assumption contradicts the information given in the theorem, which states that the total number of chocolate bars is 12.

Step-by-step explanation:

To prove the theorem by contradiction, we start by assuming that all the kids have exactly two chocolate bars each. This assumption contradicts the information given in the theorem, which states that the total number of chocolate bars is 12. If each kid has exactly two chocolate bars, the total number of chocolate bars would be 10 (5 kids multiplied by 2 chocolate bars each), not 12. Therefore, this assumption leads to a contradiction and cannot be true.