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Set Proofs without using Venn Diagrams

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3. Prove, without using Venn diagrams that
a) A intersect ( B union C) = A intersect B) union (A intersect C) and
b) A union ( B intersect C) = (A union B) intersect (A union C),
for all sets A, B, C

4. Prove, without using Venn diagrams, that the statements
i) A subset of B
ii) A intersect B = A, and
iii) A union B = B

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Set proofs are provided without using Venn diagrams.

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3. Prove, without using Venn diagrams that
a) A intersect ( B union C) = A intersect B) ...

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