equals() and hashCode() contract in Java

Question

The SCJP 6 Study Guide from Bert Bates and Kathy Sierra states on page 554 (among other requirements) that x.hashCode() != y.hashCode() requires that x.equals(y) == false.

But the Javadoc for Object doesn't mention such requirement explicitly. Quote:
If two objects are equal according to the equals(Object) method, then calling the hashCode method on each of the two objects must produce the same integer result.

Should I take what Javadoc says as a material implication, such as eq -> hc? Then there would be no conflict between these two sources.

Answer 1

The two statements are equivalent.

Put simply:

1. if two hashcodes differ, the objects are definitely different under equals.
2. if two hashcodes are the same, we don't know. (but in many practical cases the objects will be equal).

Answer 2

As z5h says, the statements are equivalent.

For logical conditions x and y, "x implies y" is the same as "!y implies !x".

"If something is a bus, it's red" is logically equivalent to "if something isn't red, it's not a bus."

This is contraposition.

Should I take what Javadoc says as a material implication, such as eq -> hc.

Yes, that's exactly what it's saying: two objects being equal under equals implies their hashcodes must be equal.