A binary operation * is defined on the set X = {1, 2, 3, 4, 5, 6} as a*b = ab + a + b. Compute 1 * 3

1. Analyze the question

You are given a binary operation defined by the rule $a * b = ab + a + b$. You need to find the result of the operation when $a = 1$ and $b = 3$.

2. Explain the concept

A binary operation is simply a rule for combining two elements of a set to produce a third element. In this case, the rule tells you to:

1. Multiply the two numbers ($a \times b$).
2. Add the first number ($a$).
3. Add the second number ($b$).
4. Sum these three results together.

3. Show the solution

Given the definition: $a * b = ab + a + b$

Substitute $a = 1$ and $b = 3$ into the formula: $1 * 3 = (1 \times 3) + 1 + 3$

Now, perform the arithmetic: $1 * 3 = 3 + 1 + 3$ $1 * 3 = 7$

4. Identify the answer

Comparing our result to the given options: A. 14 B. 4 C. 7 D. 5

The correct option is C.

5. Tip

When dealing with binary operations in JAMB, always write out the formula clearly and substitute your values inside parentheses. This prevents "sign errors" or confusion, especially when the operation involves negative numbers or more complex algebraic expressions.