1974 AMC 12 Problem 13
Attempt Problem 13 of the 1974 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 1974 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
13.
Which of the following is equivalent to “If is true then is false”?
“ is true or is false.”
“If is false then is true.”
“If is false then is true.”
“If is true then is false.”
“If is true then is true.”
Answer: D
Small hint:
An implication is equivalent to its contrapositive
Big hint:
Reverse the implication and negate both “ true” and “ false”
Solution:
The contrapositive of “ true implies false” is “ not false implies not true.” This is exactly “If is true then is false.”
Therefore, the correct answer is D.
Problem 13 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
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