Very briefly, give one example of how penelope shows fidelity to odysseus and one example of how she shows infidelity.

Penelope showed fidelity to Odysseus through simply not entertaining any other man at the time Odysseus was away, as well as managing the household devoutly and raising their son to be emulate or follow his father's legacy. 

An example of how she showed infidelity was when she was 'teasing' the suitors she had and actually considered the thought of her being a widow. But that's as close as she could get.