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schoolemailonlyno1
03.07.2019 •
Mathematics
6) let a = ℤ and r be the relation on a where a r b if and only if a + b is a multiple of 4. determine whether r is reflexive, irreflexive, symmetric, asymmetric, antisymmetric, or transitive. for each property, either explain why r has that property or give an example showing why it does not.
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Ответ:
reflexive
NO - e.g. 1+1=2 which is not a multiple of 4
irreflexive
NO - e.g. 2+2=4 which is multiple of 4
symmetric
YES - If
is a multiple of 4, then
is all multiple of 4, because addition is commutative.
antysymmetric
NO, because it's symmetric.
transitive
NO - e.g. 1+3=4 , 3+5=8 , 1+5=6 and 6 is not a multiple of 4.
Ответ:
mean
Step-by-step explanation: