Show that for any sets A and B. A=`(A cap B) cup (A - B)` and `A cup(B - A)=(A cup B)`

Is it true that for any sets A and B , P (A) cup P (B) = P(A cup B) ? Justify your answer

For any sets 'A' and 'B', show that P(A nn B)=P(A) nn P(B)

Consider the following venn diagram Using the Venn diagram, fill in the blanks by choosing correct answer from the bracket (A-B) cup (A cap B) = -----,(A - B)cup(A cap B)cup(B-A_=----- , A cup(B-A) = ----,A-(A-B)=-----[B,A,AcapB,A cupB]

Show that A cap B = A cap C need not imply B = C

Given the following result " The dual of any result in set theory will be another result, where the dual is obtained by changing ' cup to cap', 'cap to cup', 'phi to U' and ' Uto phi'" Write the dual results of the following results A cup (B cap C) = ( A cup B) cap (A cup C)