Mathematics, 08.09.2019 01:20 dan7478
Let n+2 denote the natural numbers greater than or equal to 2. let mrn if gcd(m, n) > 1. the binary relation r on n2 is
(a) reflexive, symmetric, not transitive
(b) reflexive, not symmetric, transitive
(c) reflexive, symmetric, transitive
(d) reflexive, not symmetric, not transitive (e) not reflexive, symmetric, not transitive
Answers: 2
we have that 
and then 
thus the binary relation is reflexive. To show that is symmetric note that for 
we have 
which implies the symmetric. In fact, the relation is not transitive, for example note that 
and 
but 
.
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Let n+2 denote the natural numbers greater than or equal to 2. let mrn if gcd(m, n) > 1. the bin...
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