Propositional calculus - I can't get why the answer for this test question is what it is Consider the following premises.


*

*If A = B then B = C.

*B != C.

*If C > D then D < E.

*F != G and A = B.

*A = B or C > D.


Alternatives:
a) F != G
b) F != G and D < E
c) A = B
d) B = C or D < E
e) D < E
The answer sheet says the correct alternative is B.
I am confused, because (1) and (2) seems to imply that A != B. In which case (4) would be contradictory. That's why I am wondering if the question itself is wrong.

I suspect that there is a typo on your source's part, namely being that (4) should be a disjunction. 
Making this correction, we have
(6) $A\neq B$. Take the contrapositive of (1) and applying modus ponens with (2).
(7) $C>D$. Use disjunctive syllogism on (5) with (6).
(8) $D<E$. Apply modus ponens on (3) with (7).
(9) $F\neq G$. Apply disjunctive syllogism on (modified 4) with (6).
(10) b) Conjunction between (8) and (9).
Thus b) would then indeed be a correct answer.
