Do cows fart when they produce milk?

Yesterday morning i woke up as normal, brushed my teeth and everything. Then made my way to the kitchen, opened the new box of `Kellogg's frosties` i purchased out of Morrison's around 2 days before. Well anyways i was munching away the cereal as i do almost every morning while i watched GM-TV, Suddenly this is when the thought crossed my mind, `Do cows fart when making milk?` I gently put the spoon down and could munch no more. The thought of farts and milk made me feel ill, i ended up just having toast and a cup of Tetly tea instead. If you've had this experience before, please help me find a way to overcome it? so i can get my life back on track