Advertisements
Advertisements
प्रश्न
Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = Φ.
उत्तर
Let A = {1, 2}, B = {2, 3}, C = {1, 3}
A ∩ B = {1, 2} ∩ {2, 3} = {2}
B ∩ C = {2, 3} ∩ {1, 3} = {3}
C ∩ A = {1, 3} ∩ {1, 2} = {1}
Hence, A ∩ B, B ∩ C, C ∩ A is not the empty set.
A ∩ B ∩ C = (A ∩ B) ∩ C
= {2} ∩ {1, 3} = ϕ.
APPEARS IN
संबंधित प्रश्न
Identify whether the following set is finite or infinite.
{1, 2, 3, ...}
Identify whether the following set is finite or infinite.
The set of positive integers greater than 100.
Identify whether the following set is finite or infinite.
The set of prime numbers less than 99.
State whether the following set is finite or infinite:
The set of lines which are parallel to the x-axis.
State whether the following set is finite or infinite:
The set of numbers which are multiple of 5.
State whether the following set is finite or infinite:
The set of animals living on the earth.
Which of the following sets are finite and which are infinite?
{x ∈ N : x > 5}
Which of the following sets are finite and which are infinite?
{x = ∈ N : x < 200}
Which of the following statements are true? Give reason to support your answer.
(i) For any two sets A and B either \[A \subseteq B o\text{ or } B \subseteq A;\]
Which of the following statements are true? Give reason to support your answer.
Every subset of an infinite set is infinite
Which of the following statements are true? Give reason to support your answer.
Every subset of a finite set is finite
Which of the following statements are true? Give reason to support your answer.
Every set has a proper subset
Which of the following statements are true? Give reason to support your answer.
{a, b, c} and {1, 2, 3} are equivalent sets
State whether the following statements are true or false:
\[a \subset {b, c, a}\]
State whether the following statements are true or false:
\[\left\{ a \right\} \in \left\{ a, b, c \right\}\]
State whether the following statements are true or false:
\[\left\{ a, b \right\} = \left\{ a, a, b, b, a \right\}\]
State whether the following statements are true or false:
The set {x ; x + 8 = 8} is the null set.
Write which of the following statements are true? Justify your answer.
The set of all integers is contained in the set of all set of all rational numbers.
Write which of the following statement are true? Justify your answer.
The set of all rectangle is contained in the set of all squares.
Write which of the following statement are true? Justify your answer.
The set of all real numbers is contained in the set of all complex numbers.
Write which of the following statement are true? Justify your answer.
The sets A = {x : x is a letter of the word "LITTLE"} and,B = {x : x is a letter of the word "TITLE"} are equal.
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\left\{ a, b, e \right\} \subset A\]
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[\left\{ 1 \right\} \in A\]
In a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone?
Suppose \[A_1 , A_2 , . . . , A_{30}\] are thirty sets each having 5 elements and \[B_1 , B_2 , . . . , B_n\] are n sets each with 3 elements. Let \[\cup^{30}_{i = 1} A_i = \cup^n_{j = 1} B_j = S\] and each element of S belong to exactly 10 of the \[A_i 's\]and exactly 9 of the\[B_j 's\] then n is equal to
If A and B are two finite sets, then n(A) + n(B) is equal to ______.
If A is a finite set containing n element, then number of subsets of A is ______.
Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n are, respectively ______.
