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Select the following relations on Z that are equivalence relations. ○{(a,b) ||a| = |b|} {(a,b) a²b² (mod m)} = ○{(a, b) | ab ≥ 0} {(a,b) a² +6² ≤ 2ab} {(a, b)|a>b-1}

Select the following relations on Z that are equivalence relations. ○{(a,b) ||a| = |b|} {(a,b) a²b² (mod m)} = ○{(a, b) | ab ≥ 0} {(a,b) a² +6² ≤ 2ab} {(a, b)|a>b-1}

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Select the following relations on Z that are equivalence relations. {(a, b) | |a| = |b|} {(a,b) a²b² (mod m)} = {(a, b) | ab ≥ 0} {(a,b) a² +6² ≤ 2ab} {(a, b) | a>b-1}
Transcribed Image Text:Select the following relations on Z that are equivalence relations. {(a, b) | |a| = |b|} {(a,b) a²b² (mod m)} = {(a, b) | ab ≥ 0} {(a,b) a² +6² ≤ 2ab} {(a, b) | a>b-1}
Select the following statements that are true. 1³ + 2³ + 3³ + 1/1/2+1/2+ ΟΣ;v=C(n+1,2) 01 +/+ +2022³ + - 2 = (1+2+3+...+2022)³ 1 2n 3x The function f(x) = [³2] is an one-to-one correspondence from Z to Z. If ƒ: A → P(A) is a function from a set A of cardinality 5 to the power set P(A), then f is not onto.
Transcribed Image Text:Select the following statements that are true. 1³ + 2³ + 3³ + 1/1/2+1/2+ ΟΣ;v=C(n+1,2) 01 +/+ +2022³ + - 2 = (1+2+3+...+2022)³ 1 2n 3x The function f(x) = [³2] is an one-to-one correspondence from Z to Z. If ƒ: A → P(A) is a function from a set A of cardinality 5 to the power set P(A), then f is not onto.
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