Question

Find an open sentence $P(n)$ over the domain $S=\{3,5,7,9\}$ such that $P(n)$ is true for half of the integers in $S$ and false for the other half.

   Find an open sentence $P(n)$ over the domain $S=\{3,5,7,9\}$ such that $P(n)$ is true for half of the integers in $S$ and false for the other half.

Mathematical Proofs: A Transition to Advanced Mathematics

Mathematical Proofs: A Transition to Advanced Mathematics

Gary Chartrand,… 4th Edition

Chapter 2, Problem 9

Instant Answer

Step 1

The domain given is \( S = \{3, 5, 7, 9\} \). We need to find an open sentence \( P(n) \) such that it is true for half of the integers in \( S \) and false for the other half. Since there are 4 integers in \( S \), \( P(n) \) should be true for 2 integers and Show more…

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Find an open sentence $P(n)$ over the domain $S=\{3,5,7,9\}$ such that $P(n)$ is true for half of the integers in $S$ and false for the other half.

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