# Problem Solving

## CONTENTS OF CURRICULUM UNIT 80.07.04

## Logic and Set Theory

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Set Difference
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Example.
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U = { 1,2,3,4,5,6}

A = { 1,4,5,6}

B = {1,3,4}

AB = {5,6}

Combining operations allows us to solve problems such as those below.

U = {1,2,3,4}

A = { 1,2}

B = { 2,3}

Find (A ½B)’

The part in parentheses is done first giving us the number 2. (A ½ B)’ = { 1,3,4} since these are the elements in the universe which are not in the intersection of (A½ B.)

Try the following:

(figure available in print form)

Find:

(figure available in print form)

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Solutions:
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(figure available in print form)

Additional exercises can be developed by the teacher to test understanding for set concepts presented in this unit. One such exercise is shown below.

Prove that AB = A ½B’

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Solution:
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AB = A. B’ is A which makes A ½B’ also equal to A. Since both sides of the equation equal set A we have proven that A B = A ½B’.