2.10.2. Prove for every integer n > 1: 1³ +23 + ... + n³ = (n(n+1)). 3.1.5. Let S and T be sets of three elements. How many functions are there from S to T? Why? 3.1.6. Let f : A → B be a function. Define a relation - on A as follows: a1 ~ a2 + f(a1) = f(a2). (a) Prove that (c) Describe the equivalence classes of - (f) Describe the equivalence classes of - when A = R × R, B = R and f(x,y) = x + y. is an equivalent relation on A. when A = B = R and f(x) = x².
2.10.2. Prove for every integer n > 1: 1³ +23 + ... + n³ = (n(n+1)). 3.1.5. Let S and T be sets of three elements. How many functions are there from S to T? Why? 3.1.6. Let f : A → B be a function. Define a relation - on A as follows: a1 ~ a2 + f(a1) = f(a2). (a) Prove that (c) Describe the equivalence classes of - (f) Describe the equivalence classes of - when A = R × R, B = R and f(x,y) = x + y. is an equivalent relation on A. when A = B = R and f(x) = x².
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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Transcribed Image Text:2.10.2. Prove for every integer n > 1: 1³ +23 + ... + n³ = (n(n+1)).
Transcribed Image Text:3.1.5. Let S and T be sets of three elements. How many functions are there from S to T? Why?
3.1.6. Let f : A → B be a function. Define a relation - on A as follows: a1 ~ a2 + f(a1) = f(a2).
(a) Prove that
(c) Describe the equivalence classes of -
(f) Describe the equivalence classes of - when A = R × R, B = R and f(x,y) = x + y.
is an equivalent relation on A.
when A = B = R and f(x) = x².
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