MTH202 Ass Sol

Question 1: (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.

Solution:

Suppose that S stands for Swimming.

B for Badminton and H for Hurdle Race.

   Venn diagram for the given instructions is as follows:

(b) Construct Membership Table of the following

(i) Students participating in swimming or badminton.

(ii) Students participating in swimming and badminton.

(I) Students participating in swimming or badminton.

S	B	SB
1	1	1
1	0	1
0	1	1
0	0	0

(II) Students participating in swimming and badminton.

S	B	SB
1	1	1
1	0	0
0	1	0
0	0	0

Question 2: 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)}

(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.

    

(I) Directed graph of the relation R is as follows:

 

(ii)                Is R Reflexive, Symmetric and Transitive? Justify your answer with the help of          Directed graph.

R is not reflexive because (a, a) is not present in R.

It is symmetric. We can check its condition through the graph shown above that whenever there is an arrow going from one point to a second there is an arrow going back from second to first.

It is not transitive because (a, b) is present and (b, c) is also present but (a, c) is not present and vice versa

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