In this part, you will practice creating new sets using the powerset operation. I give you a set A. Your task will be to write down P(A) by listing all its members. (i) A = The set of all possible outcomes of tossing a coin once. (ii) A = The set of all possible outcomes of tossing a coin twice.

Write the following sets in set-builder notation:(a) {58, 59, 60, · · · }(b) {13, , 14, 15, · · · , 63}(c) {7, 8, 9, 10, 11, 12, 13, 14}(d) Set E is the set of odd natural numbers.

A lock uses 3 numbers as an unlock code, each of which can be 0 to 19.  If there are no restrictions on the numbers, how many possible unlock codes are available?

Proficiency Redos Proficiency #5. [Set builder notation] a. Write the set A = {1,3, 4, 5, 7} in set builder notation without using any of the numbers in A. b. Write “the set of integers that are the product of the squares of two integers" in set builder notation, without using any words. (As an example, 36 = 2²32 is in this set.)

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