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The following set properties are
given here in preparation for the properties for addition and
multiplication in arithmetic. Note the close similarity between
these properties and their corresponding properties for addition
and multiplication.
Identity
Property for Union:
The
Identity Property for Union says that the union of a set and
the empty set is the set, i.e., union of a set with the empty
set includes all the members of the set.
General Property:
A
∪
∅
=
∅
∪
A =
A
Example:
Let A = {3, 7, 11}
and B = {x
: x is a natural
number less than 0}.
Then A
∪
B
= {3, 7, 11}
∪
{ } = {3, 7, 11}.
General Property:
A
∩
∅
=
∅
∩ A =
∅.
Example:
Let A = {3, 7, 11}
and B = {x
: x is a natural
number less than 0}.
Then A
∩ B
= {3, 7, 11}
∩ { } = { }.
What number has a similar property
when multiplying whole numbers? What is the corresponding
property for multiplication of whole numbers?