Discrete Mathematics

Set Operations

Sets - Symmetric Difference

         

Consider the sets A={x8<x<4,x is an integer}B={x2<x11,x is an integer}.\begin{aligned} A &=\{x \mid -8 < x < 4, x \text{ is an integer} \}\\ B &=\{x \mid -2 < x \leq 11, x \text{ is an integer} \}. \end{aligned} What is AB? \lvert A \triangle B \rvert ?

Details and assumptions

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Consider two sets:

A={5,6,7,8,9,10}B={6,8,10,16,24} A = \{ 5, 6, 7, 8, 9, 10 \} \\ B = \{ 6, 8, 10, 16, 24 \}

What is AB \lvert A \triangle B \rvert ?

Consider the sets A={1,2,a+7},B={a+3,a2,a+10,16}.A=\{1,2,a+7\}, B=\{a+3, a^2, -a+10, 16\}. If AB={1,16},A \cap B=\{1, 16\}, what is the sum of all the elements in the set AB?A \triangle B?

Details and assumptions

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If sets AA and BB satisfy A={23,11,55,6,4,18,37},AB={37,55},AB=5,\begin{aligned} A & =\{23, 11, 55, 6, 4, 18, 37 \},\\ A\cap B & =\{37, 55\}, \\ \lvert A \triangle B \rvert & =5, \end{aligned} what is the sum of all the elements in the set B?B?

Details and assumptions

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If AA and BB are two sets such that A=24,B=17,BA=9,|A|=24, |B|=17, |B-A|=9, what is the value of AB? \lvert A \triangle B \rvert ?

Details and assumptions

You may choose to read the summary page Set Notation.

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