Let "O" (addition) and "o" (multiplication) be two binary operations on the set V = {a | a e R} %3D defined by Va, be V, a Ð b = -ab and Vk e R, ko a = ka respectively. Then which of the following is/are always correct ? I. V is closed under addition. II. V is closed under multiplication. III. V is not commutative with respect to addition. IV. The additive identity of V is -1. (a) Only I (b) Only II (c) Only II and IV (d) Only I, II and IV (e) Only I, II and III

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 9E: 9. The definition of an even integer was stated in Section 1.2. Prove or disprove that the set of...
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Let "O" (addition) and "o" (multiplication) be two binary operations on the set V = {a | a € R}
defined by Va, b e V, a b = -ab and Vk e R, ko a = ka respectively. Then which of the following
is/are always correct ?
I. V is closed under addition.
II. V is closed under multiplication.
III. V is not commutative with respect to addition.
IV. The additive identity of V is – 1.
(a) Only I
(b) Only II
(c) Only II and IV
(d) Only I, II and IV
(e) Only I, II and II
Transcribed Image Text:Let "O" (addition) and "o" (multiplication) be two binary operations on the set V = {a | a € R} defined by Va, b e V, a b = -ab and Vk e R, ko a = ka respectively. Then which of the following is/are always correct ? I. V is closed under addition. II. V is closed under multiplication. III. V is not commutative with respect to addition. IV. The additive identity of V is – 1. (a) Only I (b) Only II (c) Only II and IV (d) Only I, II and IV (e) Only I, II and II
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