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

Answer Details

The problem gives a special binary operation defined by the formula: for any elements \( a \) and \( b \) in the set \( X = \{1, 2, 3, 4, 5, 6\} \), the operation \(*\) is defined as

\[ a * b = ab + a + b \] where \( ab \) means the ordinary multiplication of \( a \) and \( b \).

To compute \( 1 * 3 \), substitute \( a = 1 \) and \( b = 3 \) into the formula:

\[ 1 * 3 = (1 \times 3) + 1 + 3 \]
\[ = 3 + 1 + 3 \]
\[ = 7 \]

The answer comes from:

• \( 1 \times 3 = 3 \) (the product)
• Adding 1 and 3 gives two more terms: \( 1 + 3 = 4 \)
• Total: \( 3 + 4 = 7 \)

The key here is that you first multiply and then add both original numbers to that product.

So, the value of \( 1 * 3 \) under this operation is 7.