Question

Consider the set \( Q \) of rational numbers. Let \( * \) be the operation \( a * b = a + b - ab \). The identity element under \( * \) is:

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

For operations on sets, the identity element satisfies \( a * e = a \) for all elements \( a \).

Answer 1

The Correct Option is A

Step 1: Find the identity element. For an operation \( * \), the identity element \( e \) satisfies \( a * e = a \) for any \( a \). Solving \( a + e - ae = a \) gives \( e = 0 \).
Step 2: Conclusion. Thus, the identity element is 0.