For each binary operation ∗ defined below, determine whether ∗ is

1.	For each binary operation ∗ defined below, determine whether ∗ is binary, 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=ab2 (iv) On Z+, define a∗b=2ab (v) On Z+, define a∗b=ab (vi) On (R-{-1} ,define a∗b=ab+1
Answer» For each binary operation $$ defined below, determine whether $$ is binary, commutative or associative. (i) On Z, define a $$ b =a-b (ii) On Q, define $a b = a b + 1$ (iii) On Q, define $a * b = \frac{a b}{2}$ (iv) On $Z^{+}$ , define $a * b = 2^{a b}$ (v) On $Z^{+}$ , define $a * b = a^{b}$ (vi) On (R-{-1} ,define $a * b = \frac{a}{b + 1}$

For each binary operation ∗ defined below, determine whether ∗ is binary, 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=ab2 (iv) On Z+, define a∗b=2ab (v) On Z+, define a∗b=ab (vi) On (R-{-1} ,define a∗b=ab+1

Answer»

For each binary operation $*$ defined below, determine whether $*$ is binary, commutative or associative.
(i) On Z, define a $*$ b =a-b

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

(iii) On Q, define $a * b = \frac{a b}{2}$

(iv) On $Z^{+}$ , define $a * b = 2^{a b}$

(v) On $Z^{+}$ , define $a * b = a^{b}$

(vi) On (R-{-1} ,define $a * b = \frac{a}{b + 1}$