1964 AHSME Problems/Problem 12
Problem
Which of the following is the negation of the statement: For all of a certain set, ?
Solution
In general, the negation of a universal ("for all") quantifier will use an existential ("there exists") quantifier, and negate the statement inside.
In this case, we change the "For all" to "There exists", and negate the inner statement from to .
So, the negation of the original statement is "There exists an such that ". Exactly one of the two statements is true, but not both. This is the same as answer .
See Also
1964 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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