Question: Prove if Card(A)B is an injection then g:P(A)->P(B). If f:A->B is an injection since A is a subset of A and B is a subset of B, all X that is a subset of A form an injection with all Y which is a subset of B. Hence g:P(A)->P(B) is an injection. Am I correct?

For this Big Problem, we’re getting really really big: infinity! Sets that are infinitely bigdo interesting things. Here we’re going to experiment with some of them.(1) Give an example of a universal set U and a set A so that U is infinite and A is infiniteand A^c (complement of A)is also infinite. (2) Give an example of a universal set U and a set A so that U is infinite and A is infiniteand A^c (complement of A)is not infinite. (3) Give an example of a set A and a set B so that A is infinite and B is infinite andA ∩ B is also infinite. (4) Give an example of a set A and a set B so that A is infinite and B is infinite andA ∩ B is not infinite. (5) If A is infinite and B is infinite, can you find an example where A ∪ B is not infinite?Why or why not? (6) If A is infinite and B is infinite, can you find an example where A−B is not infinite?Why or why not? (7) An Interesting Fact is that there are different sizes of infinity. For example, if A is aninfinite set, then P(A) is even bigger.…

Use generating functions to find the number of ways to select50 balls from a large pile of white, blue, and green balls if(a) The selection has at least five balls of each color.(b) The selection has at most six green and at most six white balls.

Only 6b