Question

One of the partitions of the set $\left\{1, 2, 5, x, y, \sqrt{2}, \sqrt{3}\right\}$ is

• A. $\left\{\left\{1, 2, x\right\},\left\{ x, 5, y\right\}, \left\{\sqrt{2}, \sqrt{3}\right\}\right\}$
• B. $\left\{\left\{1, 2, \sqrt{2}\right\},\left\{ x, y, \sqrt{2}\right\}, \left\{5, \sqrt{2}, \sqrt{3}\right\}\right\}$
• C. $\left\{\left\{1, 2, \right\},\left\{ 5, x\right\}, \left\{\sqrt{2}, \sqrt{3}\right\}\right\}$
• D. $\left\{\left\{1, 2, 5\right\},\left\{ x, y\right\}, \left\{\sqrt{2}, \sqrt{3}\right\}\right\}$

Answer 1

Answer: (D)

For a set S, the partition of S is a set of subsets of S, such that they are pair-wise disjoint and their union is S.
In the options (a) & (b), the subsets are not disjoint. In the option (c), the subsets are disjoints but their union is not equal to the given set.
Only the option (d) meets with both the requirements.