Advertisements
Advertisements
प्रश्न
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that \[\left( A \cap B \right)' = A' \cup B'\]
Advertisements
उत्तर
Given:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}
We have to verify:
\[\left( A \cap B \right)' = A' \cup B'\]
LHS
\[A \cap B = {2}\]
\[\left( A \cap B \right)' = {1, 3, 4, 5, 6, 7, 8, 9}\]
RHS
\[A' = {1, 3, 5, 7, 9}\]
\[B' = {1, 4, 6, 8, 9}\]
\[A' \cup B' = {1, 3, 4, 5, 6, 7, 8, 9}\]
LHS = RHS
Hence proved.
APPEARS IN
संबंधित प्रश्न
Identify whether the following is set or not? Justify your answer.
A team of eleven best-cricket batsmen of the world.
Identify whether the following is set or not? Justify your answer.
The collection of all natural numbers less than 100.
Identify whether the following is set or not? Justify your answer.
The collection of all even integers.
Write the following set in roster form:
E = The set of all letters in the word TRIGONOMETRY
Write the following set in the set-builder form:
{5, 25, 125, 625}
Write the following set in the set-builder form:
{2, 4, 6, …}
List all the elements of the following set:
B = `{x : x "is an integer", -1/2 < x < 9/2}`
List all the elements of the following set:
C = {x : x is an integer, x2 ≤ 4}
List all the elements of the following set:
D = {x : x is a letter in the word “LOYAL”}
Which of the following collection are sets? Justify your answer:
The collection of prime integers.
Describe the following sets in Roster form:
{x : x is a letter before e in the English alphabet}
Describe the following sets in Roster form:
The set of all letters in the word 'Better'.
List all the elements of the following sets:
\[A = \left\{ x: x^2 \leq 10, x \in Z \right\}\]
List all the elements of the following set:
F = {x : x is a letter of the word "MISSISSIPPI"}
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\phi \subset \left\{ a, b, c \right\}\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\left\{ c, d \right\} \subset A\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[a \in A\]
Let\[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true?
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[2 \subset A\]
Write down all possible proper subsets each of the following set:
{1, 2, 3}
What is the total number of proper subsets of a set consisting of n elements?
If A is any set, prove that: \[A \subseteq \phi \Leftrightarrow A = \phi .\]
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
0 ____ A
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
10 _____ A
Describe the following set in Roster form
A = {x/x is a letter of the word 'MOVEMENT'}
There are 260 persons with skin disorders. If 150 had been exposed to chemical A, 74 to chemical B, and 36 to both chemicals A and B, find the number of persons exposed to Chemical B but not Chemical A
Answer the following:
Write down the following set in set-builder form
{a, e, i, o, u)
Answer the following:
Write down the following set in set-builder form
{Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
Answer the following:
In a school there are 20 teachers who teach Mathematics or Physics. Of these, 12 teach Mathematics and 4 teach both Physics and Mathematics. How many teachers teach Physics?
Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed in Mathematics and Science but not in English
Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed in more than one subject only
In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows:
French = 17, English = 13, Sanskrit = 15 French and English = 09, English and Sanskrit = 4 French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study none of the three languages
Let S = set of points inside the square, T = the set of points inside the triangle and C = the set of points inside the circle. If the triangle and circle intersect each other and are contained in a square. Then ______.
In a town of 840 persons, 450 persons read Hindi, 300 read English and 200 read both. Then the number of persons who read neither is ______.
