Explanation Given information: The relation R is an equivalence relation on the set A. A = {-4, -3, -2, -1, 0, 1, 2, 3, 4}. R defined on A as follows: For all ( m , n ) ∈ A , m R n ⇔ 4 | ( m 2 − n 2 ) . Calculation: A = { − 4 , − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 , 4 } R = { ( a , b ) ∈ A × A | 4 | ( a 2 − b 2 ) } Let us first determine which values are in the same equivalence class as − 4. a is in the same equivalence class as − 4, when ( − 4 , a ) ∈ R and thus when ( − 4 ) 2 − a 2 = 16 − a 2 is divisible by 4 ( ( − 4 ) 2 − a 2 = 16 − a 2 is a multiply of 4 ) . Element ( − 4 ) 2 − a 2 = 16 − a 2 in same equivalence class as − 4 − 3 16 − (- 3)2 = 16 − 9 = 7 No −2 16 − (- 2)2 = 16 − 4 = 12 Yes −1 16 − (- 1)2 = 16 − 1 = 15 No 0 16 − 0s

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Chapter 8.3, Problem 11ES

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To find the distinct equivalence classes of R.

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Chapter 8 Solutions

WEBASSIGN F/EPPS DISCRETE MATHEMATICS

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To find the distinct equivalence classes of R.

Solution Summary: The author explains that R is an equivalence relation on the set A. A = -4,-3,-2,-1, 0, 1, 2, 3, 4.

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To find the distinct equivalence classes of R.

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