Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

Please do Exercise 17.3.3 part B, C, and D and please show step by step and explain

Hint for B: You may assume (without proof) that the negative of
any integer is an integer, and that the sum of any two integers is an integer.
For transitivity, notice that x − z = (x − y) + (y − z). 

Exercise 17.3.3. Show that each of these binary relations is an equivalence relation. (a) The binary relation on R defined by x ~y iff x²-3x = y² - 3y. (b) The binary relation ~ on R defined by ay iff x - y = Z. (*Hint*) (c) The binary relation ~ on Nx N defined by (a1, b₁)~ (a2, b₂) iff a1b₂ = a2b1. (*Hint*) (d) The binary relation~ on C defined by 2₁ ~ 22 iff |2₁| = |22|.
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Transcribed Image Text:Exercise 17.3.3. Show that each of these binary relations is an equivalence relation. (a) The binary relation on R defined by x ~y iff x²-3x = y² - 3y. (b) The binary relation ~ on R defined by ay iff x - y = Z. (*Hint*) (c) The binary relation ~ on Nx N defined by (a1, b₁)~ (a2, b₂) iff a1b₂ = a2b1. (*Hint*) (d) The binary relation~ on C defined by 2₁ ~ 22 iff |2₁| = |22|.
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