Consider the following set property: For all sets A, B, and C,
Use an element argument to derive the property.
Cite a property from Theorem for every step of the proof.
Solution: Let be any sets. Then
Consider the set property,
, for any three sets .
Derive the stated property: in the method of element
In element argument method, a property can be shown, by showing
To show :
Let . Then, by the definition of set union, .
Case - :
When , by the definition of set difference, .
Since and by the definition of set union, . Also, since and by the definition
Of set interaction, .
Use an algebraic argument to derive the property (by applying properties from Theorem).
Comment on which method you found easier.
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