I'm working out of Abbott's Understanding Analysis and I'm trying to show the following,(adsbygoogle = window.adsbygoogle || []).push({});

For an arbitrary function [itex]g :\mathbb{R}\longrightarrow \mathbb{R}[/itex] it is always true that [itex]g(A\bigcap B) \subseteq g(A) \bigcap g(B)[/itex] for all sets [itex]A, B \subseteq \mathbb{R}[/itex].

I'm confused on how to get going with this--any help or hints would be greatly appreciated. Thanks.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proof on functions of an intersection of sets

Loading...

Similar Threads - Proof functions intersection | Date |
---|---|

Proof: integral of continuous function is 0 so function is 0 | Feb 10, 2016 |

Spivak Thomae's Function proof explanation | Dec 19, 2015 |

Proof Taylor series of (1-x)^(-1/2) converges to function | Jun 7, 2015 |

Proving properties of the Dirac delta function | Apr 12, 2015 |

Proper proof of a delta function | Apr 1, 2014 |

**Physics Forums - The Fusion of Science and Community**