Anchor: I have an irritation, not a problem, but I thought perhaps you could offer me a palliative.
Entailed: I would like you to offer me a palliative for my irritation. 
Contradiction: I have a problem, I do not want anything from you.
Contradiction: An artist is painting a stop sign.
Contradiction: If spending remains the same, lowering one tax automatically results in having to raise another.
Contradiction: the woman is asleep at home
Contradiction: A dog is playing with a ball.