SOLUTION: Can someone help with this?
Let σ be the relation on N defined by x σ y if and only if x ≤ y ≤ 2x.
Prove that σ is reflexive
Is σ transitiv
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Question 1046926: Can someone help with this?
Let σ be the relation on N defined by x σ y if and only if x ≤ y ≤ 2x.
Prove that σ is reflexive
Is σ transitive?
thank you very much
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
a) reflexive means a sigma a, then
:
x sigma x then x < or = x < or = 2x
:
note x = x and x < 2x
:
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sigma is reflexive
:
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b) sigma is transitive if we have
:
x sigma y and y sigma z then x sigma z
:
we have the following
:
x sigma y then x < or = y < or = 2x
:
y sigma z then y < or = z < or = 2y
:
since < or = is an ordered relation, we know
:
x < or = z and z < or = 2y but is z < or = 2x?
:
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the example is x=1, y=2, z=3
x sigma y is 1 < or = 2 < or = 2
y sigma z is 2 < or = 3 < or = 4
x sigma z is 1 < or = 3 < or = 2 *** this is false
sigma is not transitive
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