P ( A ∪ B )? Justify your answer. Fig . SETS .
Show that for any sets A and B, A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ( B – A ) = ( A ∪ B ) . Using properties of sets, show that (i) A ∪ ( A ∩ B ) = A (ii) A ∩ ( A ∪ B ) = A. . Show that A ∩ B = A ∩ C need not imply B = C.
. Let A and B be sets. If A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for some set X, show that A = B. ( Hints A = A ∩ ( A ∪ X ) , B = B ∩ ( B ∪ X ) and use Distributive law ) .
Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = φ . . In a survey of students in a school, students were found to be taking tea and taking coffee, were taking both tea and coffee. Find how many students were taking neither tea nor coffee?
. In a group of students, students know Hindi, know English and know both. Each of the students knows either Hindi or English. How many students are there in the group?
. In a survey of people, it was found that people read newspaper H, read newspaper T, read newspaper I, read both H and I, read both H and T, read both T and I, read all three newspapers. Find: (i) the number of people who read at least one of the newspapers. (ii) the number of people who read exactly one newspaper.
. In a survey it was found that people liked product A, liked product B and liked product C. If