(a) The only artery that carries deoxygenated blood is the pulmonary artery.
(b) Blood vessels are classified into arteries or veins based on the direction of the blood flow and not on the basis of oxygenated or deoxygenated blood.
Blood vessels that carries blood away from the heart are called arteries. The pulmonary artery carries blood from the heart to the lungs i.e., away from heart so it is called an artery even though it carries deoxygenated blood.