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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-> 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
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x sigma x then x < or = x < or = 2x
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note x = x and x < 2x
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sigma is reflexive
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b) sigma is transitive if we have
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x sigma y and y sigma z then x sigma z
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we have the following
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x sigma y then x < or = y < or = 2x
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y sigma z then y < or = z < or = 2y
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since < or = is an ordered relation, we know
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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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