# Transitive Property

If x < y and y < z, then x < z |

Example

If 1/*Q* > 1, which of the following must be true?

- 1 < Q2
- 1 > Q2
- Q < Q2

Solution

Since 1/

Hence,

*Q*> 1 and 1 > 0, we know from the transitive property that 1/*Q*is positive.Hence,

*Q*is positive. Therefore, we can multiply both sides of 1/*Q*> 1 by*Q*without reversing the inequality:Reducing yields | 1 > Q |

Multiplying both sides again by Q yields |
Q > Q^{2} |

Using the transitive property to combine the last two inequalities yields | 1 > Q^{2} |

The answer is (C).