Due Date: May 13, 2010

Question 1; Mark: 10
(a) Express the given information through Venn diagram.

In a high school students attended the Annual sports week, they are free to participate any of the following games: Swimming, Badminton and Hurdle race.

(i) 13 students participated in all of these games.
(ii) 36 students participated in Swimming and Badminton but not in Hurdle Race.
(iii) 28 students participated in Badminton and Hurdle Race.
(iv) 15 students participated in Swimming and Hurdle Race but not in Badminton.

(b) Construct Membership Table of the following

(i) Students participating in swimming or badminton.
(ii) Students participating in swimming and badminton.

Question 2; Marks: 10
Let A = {a, b, c, d} be a set and a relation R is defined on A as follows:

R = { (a,b), (c,b), (d,b), (a,d), ( b,b), ( b,a), ( d,a), ( b,c), ( c,c), ( b,d), ( d,d)}

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(i) Construct the Directed Graph.
(ii) Is R Reflexive, Symmetric and Transitive? Justify your answer with the help of Directed graph.
(iii) Show its Matrix Representation.