Given a universal set U and subsets A, O, and C, find the elements of each subset based on specific…

Question

Given a universal set U and subsets A, O, and C, find the elements of each subset based on specific properties (square numbers, odd numbers, composite numbers).

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the set theory problems:

1)
Given the universal set $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24\}$ .

a)

Identify square numbers less than 25.
Square numbers are numbers obtained by squaring an integer.
$1^2 = 1$
$2^2 = 4$
$3^2 = 9$
$4^2 = 16$
$5^2 = 25$ (This is not less than 25)
List the elements of set A from the universal set U.
The square numbers less than 25 that are in U are $1, 4, 9, 16$ .
$A = \boxed{\{1, 4, 9, 16\}}$
b)
Identify odd numbers from the universal set U.
Odd numbers are integers that are not divisible by 2.
List the elements of set O.
The odd numbers in U are $1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23$ .
$O = \boxed{\{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23\}}$
c)
Identify composite numbers from the universal set U.
A composite number is a positive integer that has at least one divisor other than 1 and itself. (Note: 1 is neither prime nor composite).
List the elements of set C.
The composite numbers in U are $4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24$ .
$C = \boxed{\{4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24\}}$
2)
Given the universal set $U = \{5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19\}$ .

a)
Identify even numbers from the universal set U.
Even numbers are integers divisible by 2.
List the elements of set E.
The even numbers in U are $6, 8, 10, 12, 14, 16, 18$ .
$E = \boxed{\{6, 8, 10, 12, 14, 16, 18\}}$
b)
Identify multiples of 3 from the universal set U.
Multiples of 3 are numbers that can be divided by 3 with no remainder.
List the elements of set $M_3$ .
The multiples of 3 in U are $6, 9, 12, 15, 18$ .
$M_3 = \boxed{\{6, 9, 12, 15, 18\}}$
c)
Identify prime numbers from the universal set U.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
List the elements of set P.
The prime numbers in U are $5, 7, 11, 13, 17, 19$ .
$P = \boxed{\{5, 7, 11, 13, 17, 19\}}$

Given a universal set U and subsets A, O, and C, find the elements of each subset based on specific properties (square numbers, odd numbers, composite numbers).

Step-by-step solution

Identify square numbers less than 25.

List the elements of set A from the universal set U.

Identify odd numbers from the universal set U.

List the elements of set O.

Identify composite numbers from the universal set U.

List the elements of set C.

Identify even numbers from the universal set U.

List the elements of set E.

Identify multiples of 3 from the universal set U.

List the elements of set $M_3$ .

Identify prime numbers from the universal set U.

List the elements of set P.

Still stuck on this one?

More Mathematics Questions

Given a universal set U and subsets A, O, and C, find the elements of each subset based on specific properties (square numbers, odd numbers, composite numbers).

Step-by-step solution

Identify square numbers less than 25.

List the elements of set A from the universal set U.

Identify odd numbers from the universal set U.

List the elements of set O.

Identify composite numbers from the universal set U.

List the elements of set C.

Identify even numbers from the universal set U.

List the elements of set E.

Identify multiples of 3 from the universal set U.

List the elements of set M3M_3M3​.

Identify prime numbers from the universal set U.

List the elements of set P.

Still stuck on this one?

More Mathematics Questions

List the elements of set $M_3$ .