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Discrete Mathematics

Set Operations

Union and Intersection

         

Given the sets \(A = \{2, 20, 22, 5, 13\}\) and \(B = \{6, 9, 20, 12, 22\}\), what is the sum of all the elements in \(A \cup B\)?

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Given the sets \(A = \{17, 29, 65, 1, 19\}\) and \(B = \{3, 9, 29, 101, 65\}\), what is the sum of all the elements in \(A \cap B\)?

Details and assumptions

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A survey of \(80\) students found that \(42\) of them are wearing red and \(34\) of them are wearing green. Furthermore, \(27\) of them are wearing neither red nor green. What is the number of students who are wearing red, green, or red and green?

If \[\begin{align} A &= \{x \mid x \text{ is any positive factor of } 52\} \\ B &= \{x \mid x \text{ is any positive factor of } 338\}, \end{align} \]

what is \(A \cap B?\)

Given the sets \[A=\{1,2,3,a,b\}, B=\{3,15,21\},\] if \(A \cup B=\{1,2,3,6,10,15,21\},\) what is the value of \(a+b?\)

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