CMSC 250 Lecture Notes - Lecture 5: Vacuous Truth, Prime Number, Empty Set

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There are two quantifiers we are going to talk about: there exists, for all. These are used in mathematical statements and we can use them in logic as well. This means the statement is true for every single case. The statement reads: for all x in the naturals where x is greater than 2 and x is prime, x is an odd number. This statement is true since 2 is the only even prime number. That means all other prime numbers must be odd, and since we are restricted to number above 2, we must have odd numbers. This quantifier means that there is one number that makes the statement either true or. This statement is true because if 8x=1, then x=1/8. A vacuously true statement exists when all members of a empty set have a certain property. Ex: all cell phones in the room are turned off.

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