Problem 2
(1) Let R be the relation {(0, 1), (1, 1), (1, 2), (2, 0), (2, 2), (3, 0)} defined on the set {0, 1, 2, 3}. Find the following:
1. Reflexive closure of R
2. Symmetric closure of R
(2) [8pts] Find the transitive closures of the following relations defined on the set {1, 2, 3, 4}. Use the matrix-based technique we studied in the class (see lecture 4.3), and show all your work
1. {(2, 1), (2, 3), (3, 1), (3, 4), (4, 1), (4, 3)}
2. {(1, 1), (1, 4), (2, 1), (2, 3), (3, 1), (3, 2), (3, 4), (4, 2)}
Problem 2
(1) Let R be the relation {(0, 1), (1, 1), (1, 2), (2, 0), (2, 2), (3, 0)} defined on the set {0, 1, 2, 3}. Find the following:
1. Reflexive closure of R
2. Symmetric closure of R
(2) [8pts] Find the transitive closures of the following relations defined on the set {1, 2, 3, 4}. Use the matrix-based technique we studied in the class (see lecture 4.3), and show all your work
1. {(2, 1), (2, 3), (3, 1), (3, 4), (4, 1), (4, 3)}
2. {(1, 1), (1, 4), (2, 1), (2, 3), (3, 1), (3, 2), (3, 4), (4, 2)}
Problem 2
(1) Let R be the relation {(0, 1), (1, 1), (1, 2), (2, 0), (2, 2), (3, 0)} defined on the set {0, 1, 2, 3}. Find the following:
1. Reflexive closure of R
2. Symmetric closure of R
(2) [8pts] Find the transitive closures of the following relations defined on the set {1, 2, 3, 4}. Use the matrix-based technique we studied in the class (see lecture 4.3), and show all your work
1. {(2, 1), (2, 3), (3, 1), (3, 4), (4, 1), (4, 3)}
2. {(1, 1), (1, 4), (2, 1), (2, 3), (3, 1), (3, 2), (3, 4), (4, 2)}
(2) [8pts] Find the transitive closures of the following relations defined on the set {1, 2, 3, 4}. Use the matrix-based technique we studied in the class (see lecture 4.3), and show all your work
1. {(2, 1), (2, 3), (3, 1), (3, 4), (4, 1), (4, 3)}
2. {(1, 1), (1, 4), (2, 1), (2, 3), (3, 1), (3, 2), (3, 4), (4, 2)}
note : only one question allowed per submission
Let R be the relation {(0, 1), (1, 1), (1, 2), (2, 0), (2, 2), (3, 0)} defined on the set {0, 1, 2, 3}. Find the following:
1. Reflexive closure of R
2. Symmetric closure of R
1.1. Reflexive closure of R
To make the relation reflexive we must have elements
(0,0) ,(1,1),(2,2) ,(3,3) that is element off the form (a,a) must be in the relation..
but here we dont have (0,0) ,(3,3),
so we add both to the relation
hence reflexive closure of the relation is (0,0) ,(3,3),
2. Symmetric closure :
To make the relation symmetric we must have elements
(1,0) ,(2,1),(0,2) ,(0,3) ,(1,1),(2,2) that is element off the form (a,b) & (b,a)must be in the relation..
but here we dont have (1,0) ,(2,1),(0,2) ,(0,3)
so we add both to the relation
hence symmetric closure of the relation is(1,0) ,(2,1),(0,2) ,(0,3)
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