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Test: Binary Operations - 2 - JAMB MCQ


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10 Questions MCQ Test - Test: Binary Operations - 2

Test: Binary Operations - 2 for JAMB 2024 is part of JAMB preparation. The Test: Binary Operations - 2 questions and answers have been prepared according to the JAMB exam syllabus.The Test: Binary Operations - 2 MCQs are made for JAMB 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Binary Operations - 2 below.
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Test: Binary Operations - 2 - Question 1

Let * be a binary operation on the set of real numbers defined by a * b = 2a - b. What is the value of 3 * (4 * 2)?

Detailed Solution for Test: Binary Operations - 2 - Question 1

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

Test: Binary Operations - 2 - Question 2

Consider the binary operation * defined on the set of integers by a * b = a + 2b. What is the result of (3 * 2) * 4?

Detailed Solution for Test: Binary Operations - 2 - Question 2

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

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Test: Binary Operations - 2 - Question 3

Let ⊗ be a binary operation on the set of rational numbers defined by a ⊗ b = ab + a. What is the identity element for this operation?

Detailed Solution for Test: Binary Operations - 2 - Question 3

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.

Test: Binary Operations - 2 - Question 4

For a binary operation * on a set, if a * b = b * a for all elements a and b in the set, the operation is said to be:

Detailed Solution for Test: Binary Operations - 2 - Question 4

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

Test: Binary Operations - 2 - Question 5

Consider the binary operation ∘ defined on the set of real numbers by a ∘ b = a2 + 2ab + b2. What is the value of 2 ∘ (3 ∘ 4)?

Detailed Solution for Test: Binary Operations - 2 - Question 5

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

Test: Binary Operations - 2 - Question 6

Let @ be a binary operation on the set of integers defined by a @ b = |a - b|. Which property does this operation satisfy?

Detailed Solution for Test: Binary Operations - 2 - Question 6

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

Test: Binary Operations - 2 - Question 7

Consider the binary operation ⊕ defined on the set of natural numbers by a ⊕ b = a2 - b2. Which property does this operation satisfy?

Detailed Solution for Test: Binary Operations - 2 - Question 7

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

Test: Binary Operations - 2 - Question 8

Let * be a binary operation on a set, and a be any element in the set. If there exists an element b such that a * b = a, then b is called:

Detailed Solution for Test: Binary Operations - 2 - Question 8

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

Test: Binary Operations - 2 - Question 9

Consider the binary operation ○ defined on the set of rational numbers by a ○ b = ab - b. Which property does this operation satisfy?

Detailed Solution for Test: Binary Operations - 2 - Question 9

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

Test: Binary Operations - 2 - Question 10

Let * be a binary operation on the set of integers defined by a * b = a + b + ab. Which property does this operation satisfy?

Detailed Solution for Test: Binary Operations - 2 - Question 10

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

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