91Ó°ÊÓ

In Exercises 61-68, calculate the number of distinct subsets and the number of distinct proper subsets for each set. \(\\{x \mid x\) is a day of the week \(\\}\)

In Exercises 67-80, find the cardinal number for each set. \(B=\\{x \mid x \in \mathbf{N}\) and \(2 \leq x<7\\}\)

A cheese pizza can be ordered with some, all, or none of the following set of toppings: \\{beef, ham, mushrooms, sausage, peppers, pepperoni, olives, prosciutto, onion . How many different variations are available for ordering a pizza?

Use the formula for the cardinal number of the union of two sets to solve Exercises 93-96. Set \(A\) contains 12 numbers and 18 letters. Set \(B\) contains 14 numbers and 10 letters. One number and 6 letters are common to both sets \(A\) and \(B\). Find the number of elements in set \(A\) or set \(B\).

A small town has four police cars. If a radio dispatcher receives a call, depending on the nature of the situation, no cars, one car, two cars, three cars, or all four cars can be sent. How many options does the dispatcher have for sending the police cars to the scene of the caller?

Describe how to find the number of distinct proper subsets for a given set. Give an example.

Every set has a proper subset.

If a set has 127 proper subsets, how many elements are there in the set?

Describe the three methods used to represent a set. Give an example of a set represented by each method.

In Exercises 128-135, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The set of fractions between 0 and 1 is an infinite set.