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, the set 
and the set 
as stated below:
and 
and 
, 
and 
, 
and 
.
, the following sets are derived:
and 
and 
.
.
so that the sets 
, 
, 
and 
are its subsets.
.
.
is the set of all even natural numbers less than 21 and divisible by 5;
contains all numbers less than 28 which when divided by 6 gives a remainder of 3.
and 
and illustrate the elements 
valid?
) and colors (set 
). Write the Cartesian product of the set 
and 
.
and 
apply.
, be a set containing all the letters of the English alphabet. The subsets are given as:
and 
.
. Write down 
, where 
is the powerset of 
.
. Are the sets 
and 
disjoint?
and 
and 
and 
disjoint?
and 
are given.
valid?
and 
.
. Find:
, 
, and 
and 
if;
.
, 
, 
and 
.
, how many total mappings are there from the set 
to the set 
have 128 subsets?
.
