Sets and Functions : Set Difference

Related BrainMass Solutions

• The Symmetric Difference of two Sets: A ring of sets is a non-empty class A of sets such that if A and B are in A, then A difference B and A intersection B are also in A. Show that A must also contain the empty set.

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  111265 Sets and Functions : The Symmetric Difference of Two Sets The symmetric difference of two sets A and B, denoted by A Δ B, is defined by A Δ B = ( A - B ) U ( B - A ); it is thus the union of their differences in opposite orders.

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  110242 Sets and Functions : Set Difference The difference between two sets A and B, denoted by A - B, is the set of all elements in A and not in B, thus A - B = A∩B'.

• Sets and Functions : Set Difference

  110241 Sets and Functions : Set Difference The difference between two sets A and B, denoted by A - B, is the set of all elements in A and not in B, thus A - B = A∩B'.

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  Therefore, if A and B are two sets with membership functions f(x) and g(x) respectively, then the set C = A - B has the membership function p(x) = min{f(x), 1 - g(x)}. This is shown in the attached figure.

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  Topology Sets and Functions (XLIII) Functions Let X and Y be non-empty sets and let A and B be rings of subsets of X and Y respectively.

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  Topology Sets and Functions (XV) The Algebra of Sets Ring of Sets The Symmetric Difference of two Sets A ring

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  114478 Sets and Functions : The symmetric difference of two sets The symmetric difference of two sets and , denoted by , is defined by ; it is thus the union of their differences in opposite orders.

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  So they are inverse functions of each other. The detailed solution explains the difference between the relation and function.