Test: Binary Operations - 2 - JAMB MCQ

3 * (4 * 2) = 3 * (2(4) - 2) = 3 * (8 - 2) = 3 * 6 = 2(3) - 6 = 6 - 6 = 0. Hence, the answer is 0.

(3 * 2) * 4 = (3 + 2(2)) * 4 = (3 + 4) * 4 = 7 * 4 = 7 + 2(4) = 7 + 8 = 15

For an element e to be an identity element, it should satisfy a ⊗ e = a for all elements a. By substituting a = 1 and e = 1 into the given expression, we get 1 ⊗ 1 = 1(1) + 1 = 1 + 1 = 2 ≠ 1. Hence, there is no identity element for this operation.

If a * b = b * a for all elements a and b in the set, the operation is said to be commutative.

2 ∘ (3 ∘ 4) = 2 ∘ (3² + 2(3)(4) + 4²) = 2 ∘ (9 + 24 + 16) = 2 ∘ 49 = 2² + 2(2)(49) + 49² = 2601.

The operation @ is commutative because a @ b = b @ a for all integers a and b.

The operation ⊕ does not satisfy the properties of associativity or commutativity.

If there exists an element b such that a * b = a, then b is called the inverse element of a.

The operation ○ does not satisfy the properties of associativity or commutativity.

The operation * does not satisfy the properties of associativity or commutativity.