A binary operation is said to be commutative if:a.a * b = 1 for all values of a and bb.a * b = a for all values of a and bc.a * b = b for all values of a and bd.a * b = b * a for all values of a and b

Let ‘&’ be a binary operation defined on the set N. Which of the following definitions is commutative but not associative?ans.a & b=a+ba & b=ab – 8a & b=aba & b=a-b

A binary operation is said to be distributive if:a.a * (b + c) = a * b + a * c for all values of a, b, and cb.a * (b + c) = a + b + c for all values of a, b, and cc.a * (b + c) = b * c for all values of a, b, and cd.a * (b + c) = 1 for all values of a, b, and c

The binary operation "⊙" is associative if:a.(a ⊙ b) ⊙ c = a ⊙ (b ⊙ c) for all values of a, b, and cb.(a ⊙ b) ⊙ c = a ⊙ b for all values of a, b, and cc.(a ⊙ b) ⊙ c = c for all values of a, b, and cd.(a ⊙ b) ⊙ c = 1 for all values of a, b, and c

Which of the examples below expresses the commutative law of multiplication?a.A + B = B + Ab.A • B = B • Ac.A • B = B + Ad.A • (B • C) = (A • B) • C

Let · be the binary operation on the set S = {a, b, c} dened by the multipli-cation table below:· a b ca b c cb a c cc c c cFor each s ∈ S dene an operation ∗s by x ∗s y = x · (s · y) and dene anoperation ◦s by x ◦s y = (x · s) · y. The multiplication tables for ∗a, ◦a arepartially completed below.∗a a b ca c cb c c cc c c◦a a b ca c ab c cc c c c(i) Complete the missing entries. [4 marks](ii) Can Light's Associativity test, together with the completed tables for∗a, ◦a, be used to determine whether or not the operation · is associative?If `yes', say if the operation is associative, justifying your answer; if `no',explain why not.