Relative Complement

Probability Level 1

Let $O=\{1,3,\cdots\}$ be the set of positive odd numbers.
Let $E=\{2,4,\cdots\}$ be the set of positive even numbers.
Let $\backslash$ be relative complement .

$O\backslash E=$

O

\mathbb N^*

(natural number set without

0

)

E

\phi

(empty set)

3 solutions

Kay Xspre
Mar 20, 2016

Positive integer has to be either in O or E, therefore, it is not possible for them to have any common member. O-E = O alone

展豪張
Mar 20, 2016

$O\backslash E=\{x|x\in O \wedge x\notin E\}$
Notice that $O$ and $E$ has no common elements ( $O \cap E=\phi$ ).
Therefore $O\backslash E=O$ .

Akash Patalwanshi
Jun 5, 2016

$O\E = O ∩ E^{c}$ where $E^{c}$ denotes the $E$ complement.

As $\large O = \{\ 1,3,..\}, E = \{\ 2, 4, ...\}$

$→ O\E = O ∩ E^{c} = O$

Relative Complement

3 solutions

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