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Prove the distributive law and De Morgan...

Prove the distributive law and De Morgan's law.
(i) `A cap (B cup C)=(A cap B)cup(A cap C)`
(ii) `(A cup B)'=A' cap B'`

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Distributive law: If A, B and C are any three sets, then
`A cap (B cup C)=(A cap B) cup (A cap C)`
Proof: For all `x in A cap (B cup C)`
`Leftrightarrow x in A and (x in B or x in C)`
`Leftrightarrow (x in a and x in B) or (x in A and x in C)`
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Prove A cup (B cap C)=(A cup B) cap(A cup C)

Prove (A cap B)'=(A' cup B')

Suppose A, B and C are three sets. Consider the following: (i) A cup (B cap C) = (A cup B) cap (A cup C) (ii) (A cap B) cup C = (A cup C) cap (B cup C) Which of the above is true?

The set (A cap B')cup (B cap C) equals

Let A = (a,e,i,o,u}, B={a,d,e,o,v} and C{ e,o,t, m} . Using Venn diagrams, verify the following : (i) A cup (Bcap C) =(A cup B) cap (A cup C) (ii) A cap (Bcup C) =(A cap B) cup (A capC) .

For sets (A cup B) cup ( A cap B) equals

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