Step 1: Understanding the Concept
The arch of the aorta gives off three large branches to the head and arms.
Step 2: Name them in order
The first is the brachiocephalic (innominate) trunk, which later splits into right carotid and right subclavian.
The second is the left common carotid artery.
The third is the left subclavian artery.
Step 3: Compare the options
The option with brachiocephalic, left common carotid and left subclavian matches.
Final Answer:
The aortic arch gives brachiocephalic, left common carotid and left subclavian arteries.
\[ \boxed{\text{(B) }\text{brachiocephalic, left common carotid and left subclavian}} \]