Test: Binary Operations - 1 - JAMB MCQ

Substituting the values, 3 * (−4) = 2(3) + (−4) = 6 − 4 = 2.

The addition of real numbers satisfies the commutative property, where a + b = b + a for any real numbers a and b.

Substituting the values, (−3) ∗ 2 = (−3)^2 + 2² = 9 + 4 = 13.

Division is not a binary operation on the set of integers because division by zero is not defined.

The property where a binary operation ∗ satisfies a ∗ b = b for all elements a and b is known as the identity property.

The operation ∗ is closed under the set of real numbers, which means for any real numbers a and b, a ∗ b is also a real number. Therefore, the operation satisfies the closure property.

Substituting the values, we get the following results:
1 ⊕ 1 = 1 + 1 − 1(1) = 1
1 ⊕ 2 = 1 + 2 − 1(2) = 1
1 ⊕ 3 = 1 + 3 − 1(3) = 0
2 ⊕ 1 = 2 + 1 − 2(1) = 1
2 ⊕ 2 = 2 + 2 − 2(2) = 0
2 ⊕ 3 = 2 + 3 − 2(3) = −1
3 ⊕ 1 = 3 + 1 − 3(1) = 0
3 ⊕ 2 = 3 + 2 − 3(2) = −1
3 ⊕ 3 = 3 + 3 − 3(3) = 3
Therefore, the result of the operation ⊕ is {0, 1, 3}.

Substituting the values, 4 ∗ (−2) = 4^3 − (−2)^3 = 64 − (−8) = 64 + 8 = 72.

The operation of multiplication (×) satisfies the associative property, where a × (b × c) = (a × b) × c for any numbers a, b, and c.

Substituting the values, (−3) ∗ (−5) = (−3) − (−5) = −3 + 5 = 2.