Question

If set \( S \) has 10 elements and \( A=\{(x,y):x,y\in S, x\ne y\} \), number of elements in \( A \)

• A. \( 100 \)
• B. \( 90 \)
• C. \( 80 \)
• D. \( 150 \)
• E. \( 45 \)

Hint:

Ordered pairs count = \( n^2 \), subtract equal ones.

Answer 1

The Correct Option is B

Concept: Ordered pairs.

Step 1: Total ordered pairs: \[ 10 \times 10 = 100 \]

Step 2: Exclude equal pairs: \[ (1,1),(2,2),... ⇒ 10 \]

Step 3: Subtract: \[ 100-10=90 \]

Step 4: Check condition \( x\ne y \).

Step 5: Final: \[ 90 \]