Foreach binary operation * definedbelow, determine whether * iscommuta

1.	Foreach binary operation * definedbelow, determine whether * iscommutative or associative.(i) OnZ,define a * b= a− b(ii) OnQ,define a * b= ab+ 1(iii) OnQ,define a * b (iv) OnZ+,define a * b= 2ab(v) OnZ+,define a * b= ab(vi) OnR −{−1}, define
Answer» For each binary operation * defined below, determine whether * is commutative or associative. (i) On Z, define a * b = a − b (ii) On Q, define a * b = ab + 1 (iii) On Q, define a * b (iv) On Z⁺, define a * b = 2^ab (v) On Z⁺, define a * b = a^b (vi) On R − {−1}, define

Foreach binary operation * definedbelow, determine whether * iscommutative or associative.(i) OnZ,define a * b= a− b(ii) OnQ,define a * b= ab+ 1(iii) OnQ,define a * b (iv) OnZ+,define a * b= 2ab(v) OnZ+,define a * b= ab(vi) OnR −{−1}, define

Answer»

For
each binary operation * defined
below, determine whether * is
commutative or associative.

(i) On
Z,
define a * b
= a
− b

(ii) On
Q,
define a * b
= ab
+ 1

(iii) On
Q,
define a * b

(iv) On
Z⁺,
define a * b
= 2^ab

(v) On
Z⁺,
define a * b
= a^b

(vi) On
R −
{−1}, define