Simple solution: * A and B can't both be true, which means that C is false. * If C is false, A must be false. * B and D have a paradoxical relationship, give

Simple solution: * A and B can't both be true, which means that C is false. * If C is false, A must be false. * B and D have a paradoxical relationship, given the others - if B were true, D would be true, which would make B false, so B must be false. * D is false, given A, B, C are false. * E is true, given A, B, C, D are false. * F is false because E is true (typo corrected as per comment)