Multiple choice

Let S = {1, 2, 3,........, m}, m >3. Let X1.........Xn be subsets of S each of size 3. Define a function f from S to the set of natural numbers as, f(i) is the number of sets Xj that contain the element i. That is $f(i)=\left | \left\{j \mid i\in X_j \right\} \right|$ then $ \sum_{i=1}^{m} f(i)$ is:

  1. 3m

  2. 3n

  3. 2m + 1

  4. 2n + 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Suppose, S = {1, 2, 3, 4} m = 4 X1 = { 1, 2, 3, } X2 = { 1, 3, 4} n = 2 $\therefore f(i)= f(1) + f(2) + f(3) + f(4) $ = 2 + 1 + 2 + 1 = 6 = 3 x 2 = 3n

Keep practicing — related questions