Difference between revisions of "1962 AHSME Problems/Problem 30"
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==Solution== | ==Solution== | ||
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+ | By De Morgan's Law, the negation of <math>p</math> and <math>q</math> are both true is that at least one of them is false, with the exception of the statement 1, i.e.; | ||
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+ | <math> \text{p and q are both true}.</math> | ||
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+ | The other three statements state that at least one statement is false. So, 2, 3, and 4 work, yielding an answer of 3, or <math>\textbf{(D)}.</math> |
Latest revision as of 02:55, 2 May 2020
Problem
Consider the statements:
How many of these imply the negative of the statement "p and q are both true?"
Solution
By De Morgan's Law, the negation of and
are both true is that at least one of them is false, with the exception of the statement 1, i.e.;
The other three statements state that at least one statement is false. So, 2, 3, and 4 work, yielding an answer of 3, or