why empty set is the subset of every set¿¿¿¿

[Ximonoce]

To show
that the empty set is a subset of every set.there are probably
many ways of
convincing yourself (or someone else).
this is the
case. 1. The set A is a subset of
the set B if and only if
every element of A is
also an element of B. If
A is the empty set then
A has no elements and so all of its elements
(there are none) belong
to B no matter what set
B we are dealing with.
That is, the empty set is
a subset of every set. 2. Another way of
understanding it is to
look at intersections.
The intersection of two
sets is a subset of each
of the original sets. So if {} is the empty set and A
is any set then {}
intersect A is {} which
means {} is a subset of A
and {} is a subset of {}. 3. You can prove it by
contradiction. Let's say
that you have the
empty set {} and a set A.
Based on the definition,
{} is a subset of A unless there is some element
in {} that is not in A. So
if {} is not a subset of A
then there is an element
in {}. But {} has no
elements and hence this is a contradiction, so the
set {} must be a subset
of A. An example with an
empty set and a non-
empty set might be
this: the (set of all
women who have
walked on the moon) and the (set of all
astronauts). Examine
the three arguments
above with this
example in mind.
Source:::: internet

[Amna]

Originally Posted by Ximonoce

To show
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Source:::: internet

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