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1.3 In each case, determine whether or not the given is a binary operation on the given set S. a) S=Z, a b=a+ b² b) S=Z, a b=a²b³ c) S=R, a.b= a a² +6² 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) S-the set of all 2x2 matrices with real entries, and if --(22) and b=(1²7) then a+b=(1+2+) j) S= the set of all subsets of a set X, A.B=(A^B) AB.

1.3 In each case, determine whether or not the given is a binary operation on the given set S. a) S=Z, a b=a+ b² b) S=Z, a b=a²b³ c) S=R, a.b= a a² +6² 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) S-the set of all 2x2 matrices with real entries, and if --(22) and b=(1²7) then a+b=(1+2+) j) S= the set of all subsets of a set X, A.B=(A^B) AB.

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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1.3 In each case, determine whether or not the given is a binary operation on the given set S. a) S=Z, a b=a+ b² b) S=Z, a b=a²b³ c) S=R, a.b=. a a² +6² 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) S-the set of all 2x2 matrices with real entries, and if --(32) b=(1/7). then a+b= and b= ·ritrs 1₂+16) j) Sthe set of all subsets of a set X, A.B=(AB) AB.
Transcribed Image Text:1.3 In each case, determine whether or not the given is a binary operation on the given set S. a) S=Z, a b=a+ b² b) S=Z, a b=a²b³ c) S=R, a.b=. a a² +6² 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) S-the set of all 2x2 matrices with real entries, and if --(32) b=(1/7). then a+b= and b= ·ritrs 1₂+16) j) Sthe set of all subsets of a set X, A.B=(AB) AB.
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