Fermat's Last Theorem

FIVE people make the following statements:-

(1)Either(a) 3's statement is false and 4's statement is true.
Or(b) 2's and 5's are both false.
(2)Either(a) 4's statement is false or 3's is false.
Or(b) 1's and 5's are both false.
(3)2's statement is true or 4's and 5's are both true.
Moreover, either 5's is false or 4's is true.
(4) 3's statement is false or 1's is true.
(5) Fermat's last theorem is true.

Which of these statements are true and which false? It will be found on trial that there is only one possibility. Thus, prove or disprove Fermat's last theorem.

Eureka, 9.

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