i. If there is a king in the hand then there is an ace, or if there isn’t a king in the hand then there is an ace, but not both.
ii. There is a king in the hand.
Given the above premises, what can you infer?
(In reply to re(2): Answer .... to your questions
by Ady TZIDON)
Actually, I agree with Math Man's interpretation. Math Man and I are considering both premises at once, and assuming that they could have been stated in either order. Or to say it differently, we are assuming that premise (i) is true when premise (ii) is true, but it is not necessarily true when premise (ii) is false. Under this interpretation, it must be true that "if there isn't a king in the hand, then there is an an ace." Therefore, it must be false that "if there is a king in the hand then there is an ace", because "not both" Therefore, there is no ace in the hand.
Charlie and Ady, on the other hand, are assuming that premise (i) is always true, whether or not there is a king in the hand. But this assumes that there is only one premise in the logical system, and that we later discover that there is a king in the hand and draw conclusions.
With all due respect to the puzzle author, the puzzle states that the logical system has two premises, so I believe that Math Man, not Charlie and not the puzzle author, is correct.