The Second Smallest Term

Probability Level 2

Given a set $S$ consisting of more than two distinct real numbers, which of the following represents the second smallest element?

Here, $\min(S)$ returns the smallest element of the set $S$ ; while $\max(S)$ returns the greatest element of the set $S$ .

S \setminus \{ \min(S) \}

S \setminus \{ \max(S) \}

\min(S \setminus \{ \min(S)\})

(S \setminus \{ \min(S) \} ) \cap (S \setminus \{ \max(S) \} )

1 solution

Pranshu Gaba
May 3, 2016

Let $a$ be the second smallest elements of set $S$ .

Note that if we delete the smallest element, $\min (S)$ , from set $S$ , then $a$ would become the smallest element of the set.

Set $S$ , with $\min (S)$ deleted, is denoted as $S \setminus \{\min (S) \}$ in set notation.

The element $a$ is the smallest element of set $S \setminus \{\min (S) \}$ , therefore $a = \min (S \setminus \{\min (S) \} )$ $_\square$