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In the semigroup with identity (R,) we define Va E R+, fa: (R, +) → (R, +) by Vx E R, fa (x) = ax. Let us now consider T = {fa: R→ R/ a E R+} and (t,0). So, a. It is (t,0) a monoid? b. It is (t,0) a semigroup? c. It is (t,0) commutative? d. Has (T,) identity?

In the semigroup with identity (R,) we define Va E R+, fa: (R, +) → (R, +) by Vx E R, fa (x) = ax. Let us now consider T = {fa: R→ R/ a E R+} and (t,0). So, a. It is (t,0) a monoid? b. It is (t,0) a semigroup? c. It is (t,0) commutative? d. Has (T,) identity?

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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In the semigroup with identity (R,;) we define Va E R*, fa: (R, +) → (IR, +) by Vx E R, fa (x) = ax. Let us now consider t = {fa: R → R/ a € R*} and (t,º). So, a. It is (T,0) a monoid? b. It is (T,0) a semigroup? c. It is (T,0) commutative? d. Has (T,0) identity?
Transcribed Image Text:In the semigroup with identity (R,;) we define Va E R*, fa: (R, +) → (IR, +) by Vx E R, fa (x) = ax. Let us now consider t = {fa: R → R/ a € R*} and (t,º). So, a. It is (T,0) a monoid? b. It is (T,0) a semigroup? c. It is (T,0) commutative? d. Has (T,0) identity?
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