Track / Stage 3 / 126 of 260 #126 of 2000

Problem 126

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, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

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 and solution reproduced as published; topic, difficulty and ordering added by this site.