mathgeek17
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- Oct 12, 2013
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Question ?
Please solve the following:
Let E be a Set and S the statement: "A relation on E which is symmetric and transitive must be reflective"
a) Find the fallacy in the following "proof" of S : Let a be in E. Choosing b with a ~ b, we have b ~ a. By symmetry, and so by transitivity a ~a
b) show that S is false
Hint: e = natural set , n ~ k if n times k is odd
Please solve the following:
Let E be a Set and S the statement: "A relation on E which is symmetric and transitive must be reflective"
a) Find the fallacy in the following "proof" of S : Let a be in E. Choosing b with a ~ b, we have b ~ a. By symmetry, and so by transitivity a ~a
b) show that S is false
Hint: e = natural set , n ~ k if n times k is odd
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