ii. What is the max number of 4-element-subsets of M we can select, such that intersection of any 3 of them is empty

Answer

16

Step-by-step explanation:

In order to get the max number of 4-element-subsets of we can select, such that intersection of any 3 of them is empty, we need to calculate the power of the set having four elements. Let the set containing the element be C as shown;

Let set C = {1, 2, 3, 4}

Power of the set P(C) = 2^n

n is the total number of element in the set. Since we have four elements in the set, n = 4

This means that the set A have 16 subsets. The subsets of the set are:

{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {2,3 4}. {1, 3, 4}, {1, 2, 3, 4}.

From all the subsets, it can be seen that intersection of set {1} and {2}, {1} and {2}, {3} and {3} are empty.

Hence the max number of 4-element-subsets of we can select, such that intersection of any 3 of them is empty is 16