Subjects set theory

Venn Symmetric Difference

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Venn Symmetric Difference


1. The problem asks to identify the Venn diagram that correctly represents the set expression $$ (A - B) \cup (B - A) $$. 2. The set $$ (A - B) $$ represents elements that are in set A but not in set B. 3. The set $$ (B - A) $$ represents elements that are in set B but not in set A. 4. The union $$ (A - B) \cup (B - A) $$ combines these two sets, which is the definition of the symmetric difference of A and B: elements in either A or B but not in both. 5. Examining the diagrams: - Diagram a) shades outside both circles, representing neither A nor B, which is incorrect. - Diagram b) shades both circles completely, including their intersection, which is $$ A \cup B $$ not the symmetric difference. - Diagram c) shades only the parts of A and B that do not overlap, exactly representing $$ (A - B) \cup (B - A) $$. 6. Therefore, the correct diagram is Diagram c). Final answer: Diagram c) correctly represents $$ (A - B) \cup (B - A) $$.