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a) S=Z, a b=a+b² b) S=Z, a b=a²b³

a) S=Z, a b=a+b² b) S=Z, a b=a²b³

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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1.6 For each case in Exercise 1.3 in which is a binary operation on S, determine whether is commutative and whether it is associative.
Transcribed Image Text:1.6 For each case in Exercise 1.3 in which is a binary operation on S, determine whether is commutative and whether it is associative.
a) SZ, a b=a+b² b) S=Z, a b=a²b³ c) S=R, a b= a a² + b² a²+2ab+b² a+b d) S=Z, a+b= e) S=Z, a b=a+b-ab f) S-R, a b=b g) S={1, -2,3,2,-4), a b= |b| h) S(1,6,3,2, 18), a+b=ab. i) Sthe set of all 2x2 matrices with real entries, and if b= (³/₁ and 7) then --(3) 2) r₁+rs √₂+16) r3+1 4+rg, (+7) j) S the set of all subsets of a set X, A. B=(A^ B) AB. a.b= 21
Transcribed Image Text:a) SZ, a b=a+b² b) S=Z, a b=a²b³ c) S=R, a b= a a² + b² a²+2ab+b² a+b d) S=Z, a+b= e) S=Z, a b=a+b-ab f) S-R, a b=b g) S={1, -2,3,2,-4), a b= |b| h) S(1,6,3,2, 18), a+b=ab. i) Sthe set of all 2x2 matrices with real entries, and if b= (³/₁ and 7) then --(3) 2) r₁+rs √₂+16) r3+1 4+rg, (+7) j) S the set of all subsets of a set X, A. B=(A^ B) AB. a.b= 21
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