Discrete Mathematics - 2 | Practice sets
UNIT-1: - SETS, RELATIONS AND FUNCTIONS
SETS
Practice – 1: Describe each of the following sets by listing its elements.
a.
{x | x is an odd positive integer
and 3 < x ≤ 7}
b.
{x | x is a month with exactly 30
days}
c.
{x | x is the capital of the United
States}
Solutions: -
a.
{x | x is an odd positive integer
and 3 < x ≤ 7}
Let A
= {x | x is an odd positive
integer and 3 < x ≤ 7}
A = {4, 5, 6, 7}
Here x is an integer number greater than 3 and
less than equal to 7, So we may write the set A as
A = {4, 5, 6, 7}
b.
{x | x is a month with exactly 30
days}
Let A = {x | x is a
month with exactly 30 days }
A month has either 28, 29, 30, or 31 days . Out
of 12 months in a year which are with exactly 30 days are : -
April, Jun, September, November.
Hence, we may write the set as : -
A = {4, 5, 6, 7}
c.
{x | x is the capital of the United
States}
Let A = {Washington D.C}
Practice – 2 :- Describe each of the following sets giving a characterizing property.
a. {1,
4, 9, 16}
b. {2, 3, 5, 7, 11, 13, 17,…}
Soln:-
a. {1, 4, 9, 16}
Let A = { 1, 4, 9, 16}
= {1, 4, 9, 16}
Here 1,
4, 9, 16 are the square roots of the 1, 2, 3, 4 and natural numbers.
Hence, we may write the set A as
A = {x :
x is the square of the all-Natural numbers}
A = {x :
x = n2 Where n ∈ N}
b.
{2, 3, 5, 7, 11, 13, 17,..}
Let A = {2,
3, 5, 7, 11, 13, 17,..}
Here 2, 3,
5, 7, 11, 13, 17,.. are set of all
positive integer number . Hence , we may write the set A as
A = {x : x
is the of set of all positive integer number}
