Question

Given set A=1,2,3,4,5,6, which of the following options forms a partition of A?

a) 1,2, 2,3,4, 4,5,6.
b) 1, 2,3,6, 4,5.
c) 1,2,3, 4,5,6
d) 1,2,3, 2,3,4,5,6.

Answer 1

To determine which option forms a partition of set A, we need to check if all the options satisfy the condition of a partition. The correct answer is option c) 1,2,3, 4,5,6.

Step-by-step explanation:

A partition of a set is a grouping of the elements of the set into non-empty subsets, such that each element is present in exactly one subset. In this case, the set A is given as {1,2,3,4,5,6}. To determine which option forms a partition of A, we need to check whether all the options satisfy the condition of a partition.

Option a) does not form a partition because it repeats some elements. Option b) forms a partition as it consists of non-empty subsets {1,2,3} and {4,5,6}. Option c) also forms a partition as it consists of non-empty subsets {1,2,3,4,5,6}. Option d) does not form a partition because it repeats some elements.

Therefore, the correct answer is option c) 1,2,3, 4,5,6.