Determine whether the given definition of ∗ give a binary operation on the given set. If so, check whether ∗ is i) commutative ii) associative? Also, examine ∗ for identity element? a. On Z + , a ∗ b = 2^ab b. On Q, a ∗ b = ?b/2 c. On Z + , a ∗ b =a^b
Determine whether the given definition of ∗ give a binary operation on the given set. If so, check whether ∗ is i) commutative ii) associative? Also, examine ∗ for identity element? a. On Z + , a ∗ b = 2^ab b. On Q, a ∗ b = ?b/2 c. On Z + , a ∗ b =a^b
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 13E: Assume that is an associative binary operation on the non empty set A. Prove that a[ b(cd) ]=[...
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Determine whether the given definition of ∗ give a binary
operation on the given set. If so, check whether ∗ is i) commutative
ii) associative? Also, examine ∗ for identity element?
a. On Z
+
, a ∗ b = 2^ab
b. On Q, a ∗ b =
?b/2
c. On Z
+
, a ∗ b =a^b
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