1962 AHSME Problems/Problem 30
Consider the statements:
How many of these imply the negative of the statement "p and q are both true?"
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