Translate the following sentence into symbolic form and form a truth table for it.

Question

The bear ate honey or fish. If the bear ate fish, then it did not eat honey. Hence, it is not the case that the bear ate honey.

Answer 1

This is an example of an 'exclusive OR'. By the first sentence, we know that there bear ate something, at least one of which was fish or honey. Without the second sentence, it would be possible for the bear to have eaten both but that second sentence eliminates the possibility: if the bear ate fish, it did not eat honey and this implies if the bear ate honey, it did not eat fish. However, the third case is not upheld, since it possible that the bear DID eat honey - merely if it did, it did not eat fish.