In 1-8, a number of relations are defined on the et A={0,1,2,3}. For each relation:
- Drae the directed graph.
- Determine whethrer the relation is reflexive.
- Determine whether the relation is symmetric.
- Determine whether the realtion is transitive.
Give a counter example in each case in which the relation does not satisfy one of the properties.
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WEBASSIGN F/EPPS DISCRETE MATHEMATICS
- In each of the following parts, a relation is defined on the set of all human beings. Determine whether the relation is reflective, symmetric, or transitive. Justify your answers. xRy if and only if x lives within 400 miles of y. xRy if and only if x is the father of y. xRy if and only if x is a first cousin of y. xRy if and only if x and y were born in the same year. xRy if and only if x and y have the same mother. xRy if and only if x and y have the same hair colour.arrow_forwardDoes the relation is a friend of have a reflexive property consider one person? A symmetric property consider two people? A transitive property consider three people?arrow_forwardThe domain of a relation R is the set of integers. x is related to y under relation R if x relation R. = y . Select the description that accurately describes a. Symmetric b. Anti-symmetric C. Anti-reflexive d. Reflexivearrow_forward
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- Determine if the relation R = {(1,3), (1,4), (2,3), (2,4), (3,4)} is reflexive, symmetric, antisymmetric, or transitive.arrow_forwardLet A = {1, 3, 5, 7,9}, B = {2, 4, 6, 8}; a R b if and only if b< a a) Find Domain of the relation R b) Find Range of the relation Rarrow_forwardii. Determine whether the relation, R = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)} is: Yes/No Justify your answer. Types of relations Reflexive Symmetric Antisymmetric Transitive (8 marks)arrow_forward
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