Show that the following four conditions are equivalent :
(i) A ⊂ B (ii) A – B = Φ (iii) A ∪ B = B (iv) A ∩ B = A

Match the following : (b)(ii)

Consider the sets φ, A = { 1, 3 }, B = {1, 5, 9}, C = {1, 3, 5, 7, 9} . Insert the symbol ⊂ or ⊄ between each of the following pair of sets: (i) φ . . . B (ii) A . . . B (iii) A . . . C (iv) B . . . C

Consider the experiment of rolling die. Let A be the event 'getting a prime number'. B be the event 'getting an odd number'. Write the sets representing the events (i) A or B (ii) A and B (iii) A but not B (iv) 'not A'.

Show that for any sets A and B, A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ( B – A ) = ( A ∪ B )

Show that A ∪ B = A ∩ B implies A = B

Show that if A ⊂ B , then C – B ⊂ C – A .

Let A= {a,b,c}. Which of the following is not an equivalence relation in A?

For any sets A and B, show that P ( A ∩ B ) = P ( A ) ∩ P ( B ) .

Consider the sets phi, A={1,3}, B={1,5,9}, C={1,3,5,7,9} . Insert the symbol subset or cancel(subset) between each of the following pair of sets. (i) phi ....B (ii) A....B (iii) A.....C (iv) B.....C