Description
Sets and Subsets
1. Determine the number of distinct sets and the number of proper subsets for each of the following:
a. (x1x and 2 < x < 6)
b. (2,4.6.8)
2. In a group of 100 customers at Pizza Inn, 80 of them ordered peppers on their pizza and 72 of them ordered sausage, 60 customers ordered both peppers and sausage on their pizza. Given this information, answer the following questions. (Hint: use a Venn Diagram)
a. How many customers ordered peppers but no sausage?
b. How many customers ordered sausage but no peppers?
c. How many customers ordered neither peppers nor sausage on their pizzas?
3. Give the cardinality of:
a. The set of all the world's oceans.
b. Set A = (1,3,4,5,6,7,11,12,13)
Requirements of the paper:
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Explanation & Answer
Attached.
Sets and Subsets
1. Determine the number of distinct sets and the number of proper subsets for each of the following:
a. (x1x and 2 < x < 6)
b. (2, 4.6.8)
Explanation
Set A is a proper subset of set B, symbolized A ⊂ B, if and only if all of the elements of set A are
elements of set B and set A ≠ B (that is, set B must contain at least one element not is set A).
The number of distinct subsets of a finite set A is 2n, where n is the number of elements in set A.
Solution
a. There are no elements in x1x that are in 2 < x < 6 therefore,...
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