Question

Prove the distributive law of intersection over the union of n sets by induction

Answer 1

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Answer 2

The distributive law of intersection over the union of n sets by induction (A^(BUC))=(A^B)U(A^C).

• Let x be an arbitrary element of A^(BUC). This means that x belongs to A and x belongs to (BUC) we know that x belongs to B or x belongs to C.
• This implies x belongs to (A^B) or x belongs to (A^C) depending on whether x belongs to B or x belongs to C.
• since x belongs to (A^B) or x belongs to (A^C), we have x belongs to (A^B)U(A^C).
• Thus A^(BUC)C (A^B)U(A^C). Hence proved.