Anchor: Fearing his powers might be waning as he approached 30, Nash decided he would solve the most important unresolved problem in  the Riemann Zeta conjecture.
Entailed: Nash though that his powers might be waning as he got closer to 30. 
Contradiction: Nash thought that his powers would increase the closer he got to 30. 
Contradiction: The man is only playing one instrument.
Contradiction: A professional woman should dress like a professional woman, in a classic style which is not overly feminine.
Contradiction: The fence was opened just now by the dog from next door.
Contradiction: Why are you questioning?