Anchor: For the third and fourth quintiles, Social Security still serves as the most important source of retirement income.
Entailed: Social security is still the most important source of retirement income for the 3rd and 4th quintiles. 
Contradiction: The third and fourth quintiles have no connection to social security when it comes to their sources of retirement income. 
Contradiction: The dog is walking aimlessly around the city searching for food.
Contradiction: Parents prefer to seek out donors with a series of desirable characteristics. 
Contradiction: The giants are resting peacefully.
Contradiction: The deep, dark, and less ephemeral are his concerns.