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. Let (A, *) be an algebraic system such that for all a, b in A Given (a b) a = a and (a b) b = (b ★ a) ★ a Show that for all a and b, (i) a (a b) = a ★b and (ii) a a= (a b) (a b) Note that an algebraic system may not be associative. Also, evaluation in an algebraic system can be assumed to be from left-to-right and hence, (a * b) ★ a = a*b* a

. Let (A, *) be an algebraic system such that for all a, b in A Given (a b) a = a and (a b) b = (b ★ a) ★ a Show that for all a and b, (i) a (a b) = a ★b and (ii) a a= (a b) (a b) Note that an algebraic system may not be associative. Also, evaluation in an algebraic system can be assumed to be from left-to-right and hence, (a * b) ★ a = a*b* a

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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2. Let (A,) be an algebraic system such that for all a, b in A Given (a b) a = a and (a*b) b = (b ★ a) * a (ii) a *a = (a * b) * (a*b) Note that an algebraic system may not be associative. Also, evaluation in an algebraic system can be assumed to be from left-to-right and hence, (a * b) ★ a ab a Show that for all a and b, (i) a (a * b) = a ★b and
Transcribed Image Text:2. Let (A,) be an algebraic system such that for all a, b in A Given (a b) a = a and (a*b) b = (b ★ a) * a (ii) a *a = (a * b) * (a*b) Note that an algebraic system may not be associative. Also, evaluation in an algebraic system can be assumed to be from left-to-right and hence, (a * b) ★ a ab a Show that for all a and b, (i) a (a * b) = a ★b and
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