1962 AMC 12 Problem 30
Attempt Problem 30 of the 1962 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 1962 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
30.
Consider the statements:
and are both true
is true and is false
is false and is true
is false and is false.
is true and is false
is false and is true
is false and is false.
How many of these imply the negation of the statement “ and are both true”?
Answer: D
Small hint:
The negation fails only when both statements are true
Big hint:
Check which of the four listed truth assignments are not case
Solution:
The negation of “ and are both true” holds whenever at least one of and is false. This occurs in cases and for a total of
Thus, the correct answer is D.
Problem 30 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 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
- 1963 AMC 12
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- 1999 AMC 12