Show that the following four conditions are equivalent: i) `A sub B`
ii) `A-B=phi`
iii) `A uu B=B`
iv) `A nn B= A`

Which of the following is equal to (A-B) uu (B-A)

Prove that A uuB=A nn B if A=B .

Two dice are thrown. The events A , B and C are as follows. A : getting an even number on the first die B : getting an odd number on the first die. C : getting the sum of the number on the dice le 5 Describe the events (i) A ′ (ii) not B (iii) A or B (iv) A and B (v) A but not C (vi) B or C (vii) B and C (viii) A∩B ′∩C ′

Show that A uu B=A nn B implies A=B

Examine whether the following statement are true or false {a} sub {a,b,c}

A and B are two events such that P(A) ne 0 . Find P(B | A) , if i) A subset B ii) A nn B=phi

Consider the sets phi , A={1,3}, B={1,5,9}, C={1,3,5,7,9}' Insert the symbol subset and not subset between each of the following pair of sets. (i) phi …. B ' (ii) A ... B (iii) A ... C (iv) B ... C

Show the following by Venn diagrams: (i) A uu B, A nn B, A-B, B-A , where A={1,3,4,6,9} and B={3, 4, 5, 8, 1 1, 1 2} (ii) A', where U={1,2,…...10} and A={2,3,6}

Find the union of each of the following pairs of sets: i) X={1,3,5} Y={1,2,3} ii) A={a, e, i, o, u}, B={a, b, c} 'iii) A={x: x is-a natural number and multiple of 3} B={x: x is a natural number less than 6} iv) 'A={x: x is a natural number and '1 B={x: x is a natural number and '6 v) 'A={1, 2,3}, B= {phi}