Disagree
Part of speech: verb
Definition: to not agree
Example sentence: Ted Cruz is a patriot. He believes in what he does. He's done marvels in mobilizing conservatives, mobilizing Americans concerned about the direction of the ever-expanding entitlement state under Obama, and particularly the threat it is to freedom. I disagree with his tactics, but I agree entirely with his objectives.
Discord
Part of speech: verb
Definition: To disagree; to be at variance; to fail to agree or harmonize; clash.
Part of speech: noun
Definition: Lack of concord, agreement or harmony among persons, groups, or things.Tension or strife resulting from a lack of agreement; dissension.An inharmonious combination of simultaneously sounded tones; a dissonance.Any harsh noise, or confused mingling of sounds.
Example sentence: Medicine is the restoration of discordant elements; sickness is the discord of the elements infused into the living body.