1953 AMC 12 Problem 40
Attempt Problem 40 of the 1953 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1953 AMC 12 solutions, or check the answer key.
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40.
The negation of the statement “all men are honest,” is:
no men are honest
all men are dishonest
some men are dishonest
no men are dishonest
some men are honest
Answer: C
Small hint:
To disprove a universal statement, only one counterexample is needed
Big hint:
Negating “every man is honest” asserts that at least one man is not honest
Solution:
The negation of “every man is honest” is “there exists a man who is not honest.” In the language of the choices, some men are dishonest.
Thus, the correct answer is C.