Given the relation on {1,2,3,4} represented by the following zero-one matrix: a.

Question

Given the relation on {1,2,3,4} represented by the following zero-one matrix:

a.)  Is it reflexive?  _______  If not, what ordered pairs must be added to make it reflexive?

b.)  Is it symmetric?  ______ If not, what ordered pairs must be added to make it symmetric?

c.)  Is it antisymmetric?  _______  If not, explain the minimum number of additions or removals necessary to make it antisymmetric?

Given the relation on {1,2,3,4} represented by the following zero-one matrix: Is it reflexive? _______ If not, what ordered pairs must be added to make it reflexive? Is it symmetric? ______ If not, what ordered pairs must be added to make it symmetric? Is it antisymmetric? _______ If not, explain the minimum number of additions or removals necessary to make it antisymmetric?

Explanation / Answer

a) No, its not reflexive... (3, 3) should be added to make it reflexive.

b) No, its not symmetric... (2, 4), (3, 1) and (4, 3) should be added to make it symmetric.

c) No, its not antisymmetric... Minimum number of additions or removals required is 3 (1 addition + 2 removals)

The antisymmetric matrix looks like(see the bold elements in the matrix for changes):

1 1 1 1

0 1 1 0

0 0 0 1

0 1 0 1

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