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1. determind if the given statement is true or false. 2.if the statement is a th

ID: 3028645 • Letter: 1

Question

1. determind if the given statement is true or false.

2.if the statement is a theorem determine if the proof? is valid

3. if the given statement is false, provide a counterexample.

hint: Problem 26. The statement x y/R is equivalent (using my notation) to the statement x [y]. Both of them mean that x belongs to the equivalence class of y with respect to the equivalence relation R.

26. Statement. Theorem? Proof? A. y, z E A. Statement: Let R be an equivalence relation on And, let z, If r e y/R and 2 r/R, then 2 y/R. Suppose z E y/R, Proof? We prove this theorem by contradiction. is symmetric, z g r/R, and z E y/R. z E y/R, since R That is, TRy also. Since y/R, yRz, since R is transitive, rR2. z e T/R. This contradicts the hypothesis z I/R.

Explanation / Answer

the given theorem and proof is correct and already proof is given.So nothing to prove in that