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.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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.
Problem 40 in Other Years
1950 AMC 12 · 1951 AMC 12 · 1952 AMC 12 · 1954 AMC 12 · 1955 AMC 12 · 1956 AMC 12 · 1957 AMC 12 · 1958 AMC 12 · 1959 AMC 12 · 1960 AMC 12 · 1961 AMC 12 · 1962 AMC 12 · 1963 AMC 12 · 1964 AMC 12 · 1965 AMC 12 · 1966 AMC 12 · 1967 AMC 12