Formulating if-then constraints in linear binary programming

From a stock of various computer accessories of different brands, the optimization problem requires deciding to keep or discard products. I am struggling to formulate the following if-then conditions:

1. If one product of a certain brand is eliminated than all the products of that brand should be eliminated.
2. If any mouse (of any brand/model) is to be kept, then at least two different models of keyboards will also be kept.
3. If any model of product X or product Y is to be kept, then all models of product Z of brand A will also be kept.