necessary vs sufficient conditions

x's being a female is a sufficient condition for x's being a mother

false

x's being a mother is a necessary condition for x's being a female

false

x's being a rectangle is a sufficient condition for x's being a square

false

x's being a square is a necessary condition for x's being a rectangle.

false

x's being greater than 15 is a necessary condition for x's being less than 20

false

x's being greater than 15 is a sufficient condition for x's being less than 20.

false

x's being less than 12 is a necessary condition for x's being less than 20

false

x's being less than 20 is a necessary condition for x's being greater than 15.

false

x's being less than 20 is a sufficient condition for x's being greater than 15

false

x's being less than 20 is a sufficient condition for x's being less than 12

false

x's having two arms is a necessary condition for x's being a human being

false

x's having two arms is a sufficient condition for x's being a human being

false

x's wanting to do a is a necessary condition for x's doing a

false

x's wanting to do a is a sufficient condition for x's doing a

false

x's being a female is a necessary condition for x's being a mother

true

x's being a mother is a sufficient condition for x's being a female.

true

x's being a rectangle is a necessary condition for x's being a square

true

x's being a square is a sufficient condition for x's being a rectangle

true

x's being an equilateral rectangle is a necessary condition for x's being a square

true

x's being an equilateral rectangle is a sufficient condition for x's being a square

true

x's being less than 12 is a sufficient condition for x's being less than 20

true

x's being less than 20 is a necessary condition for x's being less than 12

true