Prove [1, Theorem 11.1.7]: Suppose that X and Y are nonempty finite sets of the same cardinality. Then a function X → Y is an injection if and only if it is a surjection. [Hint: Use the pigeonhole principle and proof by contradiction.]

What is the equation and solution for the sentence? the sum of a number and thirty-one is one hundred thirteen. write the equation as n-31=113 and subtract 31 from both sides. the answer is 82. write the equation as n+31=113 and subtract 31 from both sides. the answer is 82. write the equation as n+31=113 and add 31 to both sides. the answer is 144. write the equation as n-31=113 and add 31 to both sides. the answer is 144.

Are triangles the congruent? write the congruency statement.what is the congruency that proves they are congruent? what is the perimeter of ∆pqr?

The cross-sectional areas of a right triangular prism and a right cylinder are congruent. the right triangular prism has a height of 6 units, and the right cylinder has a height of 6 units. which conclusion can be made from the given information? the volume of the triangular prism is half the volume of the cylinder. the volume of the triangular prism is twice the volume of the cylinder. the volume of the triangular prism is equal to the volume of the cylinder. the volume of the triangular prism is not equal to the volume of the cylinder.