S.O.S. Mathematics CyberBoard

Hi, I have a question and have worked it out as below. Can you tell me if I am right.

Q. Let friend (x,y) denote 'x is a friend of y, man (x) 'x is a man' and woman (y) 'y is a woman'. Translate the following formulas into English sentences:

i) ∀x∃y friend(x,y)

Answer: Every man has atleast one woman friend.

ii) ∃x (man(x) ^ ∀y (friend(x,y) --> woman(y)))

Answer: For all friendship groups in the world, there is atleast one man and woman a friend.

Thanks and Regards
Jordan