Question

two sets that have no common elements are known as​

Answer 1

Two sets that have no common elements are known as​ disjoint sets.

Step-by-step explanation:

• Disjointed sets have no common elements because the intersection set function between them will always result in a zero (null) set or blank set.  

Let us consider two different sets of $X =$ {$a,b$ } and $Y =$ {$c, d$}.

• It is clear that there are no common elements between these two sets. 

• The intersection of these two sets $X$ and $Y$ can be written as:

         $X$ ∩ $Y=$ Ф.

• Thus, it can be said that the intersection function of the separation sets gives a null set.

For example, $P$$=$ {$1, 2$}, $Q=$ { $2,3$ } and $R=${ $5, 3$ }. Let's determine if any of these sets are disjoint sets.

The first step is to perform the intersection operation on each pair of sets.

$P$ ∩ $Q$ $=${ $1, 2$ } { $2, 3$ }

$P$ ∩ $Q=$ {$2$ }

And,

$Q$ ∩ $R$ $=$ { $2, 3$ } ∩ { $5,3$ }

$Q$ ∩ $R$ $=$ { $3$ }

And then the last pair,

P ∩ R = {$1, 2$} ∩ { $5, 3$ }

$P$ ∩ $R=$ Ф

So, among the given sets, $P$ and $R$ can be considered as disjoint sets.