Let A 1 2 12 Give an example of a partition S of A satisfy

Let A = {1, 2, ..., 12}. Give an example of a partition S of A satisfying the following requirements: |S| = 5, there is a subset T of S such that |T| = 4 and | _X T X| = 10 and there is no element B S such that |B| = 3.

Solution

i) partition of a set is grouping the sets elements into non empty subsets.

A={1,2,3,4,5,........,12}

Cardinal of S is to be 5. So let S={4,5,6,7,8} that is it contains 5 elements of A

ii) and T is subset of S with cardinality 4. So T={4,5,6,7} and atleast one element of T is X. And X has cardinality 10 that means X contains atleast one element of T and it has 10 elements

X={4,5,6,7,13,14,15,16,17,18,19}

iii)no element of B belongs to S and B has 3 elements because given it has cardinality of 3. So B={9,10,11}