# Discrete Structures

**brinco**

- Translate the following English sentences into statements of predicate calculus.
All programmers enjoy discrete mathematics

Some integers are not odd

Every integer that is divisible by 2 is even

There exists a natural number that is not a positive integer

- Refer to the statements of predicate calculus you provided for problem 1. Write the negation of each of those statements.
- Give counterexamples to show each of the following is false:
For all positive integers x and y, xy > x + y

For all real numbers x, x > 1/x

- Translate the following English sentences into statements of predicate calculus that contain double quantifiers:
Any even integer is equal to twice some other even integer

- Some natural number is no bigger than every natural number
Refer to the statements in problem 4 and indicate whether each is true or false. Provide your reasoning.

- 9 years ago
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