Please show stepbystep solutions this is discrete math 2 0 0

Please show step-by-step solutions, this is discrete math 2.

0 0 (5 pnts each) 5) Let R be represented by the matrix MR 1 0 1 1 1 0 (a) Give the matrix that represents the reflexive closure of R, r(R): (b) Give the matrix that represents the symmetric closure of R s(R):

Solution

a) For the reflexive closure all (a,a) should belong to the matrix

Hence the matrix for the reflexive closure will be

b) For the symmetric closure, if (a,b) belongs to R, then (b,a) must also belong to R

(2,1) belongs to R, so (1,2) should also belong to R

(2,3) belongs to R, so (3,2) should also belong to R

(3,1) belongs to R, so (1,3) should also belong to R

(3,2) belongs to R, so (2,3) should also belong to R

1	0	0
1	1	1
1	1	1