Track / Stage 3 / 146 of 260 #146 of 1964

Problem 146

AMC 10/12, early questions

Combinatorics Difficulty 3.4 Prove it

Use the method of contradiction to prove "Among three real numbers a, b, and c, at most one is positive". The correct assumption among the following is (　　)
A: Two numbers are positive
B: All three numbers are positive
C: At least two numbers are negative
D: At least two numbers are positive

This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.

Official solution

Solution: According to the method and steps of proving a mathematical proposition by contradiction, we should first assume that the negation of the proposition to be proved holds.
The negation of the proposition "Among three real numbers a, b, and c, at most one is positive" is "At least two numbers are positive",
Therefore, the correct choice is $\boxed{\text{D}}$ .
Analysis: First, find the negation of the proposition "Among three real numbers a, b, and c, at most one is positive" to reach the conclusion.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.