Q

# For each operation ∗ defined below, determine whether ∗ is binary, commutative or associative. On Z, define a ∗ b = a – b

Q2. For each operation ∗ defined below, determine whether ∗ is binary, commutative
or associative.

(i)On $Z$, define $a * b = a-b$

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a*b=a-b

b*a=b-a

$a*b\neq b*a$

so * is not commutative

(a*b)*c=(a-b)-c

a*(b*c)=a-(b-c)=a-b+c

(a*b)*c not equal to a*(b*c), so * is not associative

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