All arteries carry oxygenated blood from the heart to the body's tissues and organs, and all veins return oxygen-depleted blood back to the heart.
The statement is false.
The cardiovascular system is composed of two circulatory paths: pulmonary circulation and systemic circulation.
In pulmonary circulation, the pulmonary artery carries deoxygenated blood from the heart into the lungs, and the pulmonary vein delivers oxygenated blood from the lungs to the heart to be pumped into systemic circulation.
It is in the systemic circulation only that arteries carry oxygenated blood away from the heart, into the body, and veins return deoxygenated blood back to the heart.
So again the answer is "false" because the pulmonary artery carries deoxygenated blood away from the heart and the pulmonary vein carries oxygenated blood to the heart.