1.Previous
3.Next

(C->A)->E is true.

C->A is false, so C is true.

The value of B does not matter, so we can arbitrarily choose it to be true.

Summing up, the valuation that sets B, C and D to be true and A, E and F to be false will make [(A->B)->((C->A)->E)]->([F->((C->D)->E)]->[(A->F)->(D->E)]) false. So it is not a tautology.

Example of a tautology:

Suppose ((A->B)->C)->((C->A)->(D->A)) is false.

Then (A->B)->C is true; C->A is true; D is true; and A is false.

Since A is false, A->B is true. So C

1.Previous
3.Next