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.
Advertisements
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.
The set of months of a year
Identify whether the following set is finite or infinite.
{1, 2, 3, ...}
Identify whether the following set is finite or infinite.
{1, 2, 3, ... 99, 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 circles passing through the origin (0, 0).
Which of the following sets are finite and which are infinite?
Set of letters of the English Alphabets
Which of the following sets are finite and which are infinite?
{x ∈ R : 0 < x < 1}.
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 set has a proper subset
Which of the following statements are true? Give reason to support your answer.
{a, b, a, b, a, b, ...} is an infinite set
Which of the following statements are true? Give reason to support your answer.
A set can have infinitely many subsets.
State whether the following statements are true or false:
\[a \subset {b, c, a}\]
State whether the following statements are true or false:
\[\left\{ a, b \right\} = \left\{ a, a, b, b, a \right\}\]
State whether the following statements are true or false:
The set {x ; x + 8 = 8} is the null set.
Decide among the following sets, which are subsets of which:
\[A = {x : x \text{ satisfies } x^2 - 8x + 12 = 0},\]
\[B = \left\{ 2, 4, 6 \right\}, C = \left\{ 2, 4, 6, 8, . . . \right\}, D = \left\{ 6 \right\} .\]
Write which of the following statement are true? Justify your answer.
The set of all crows is contained in the set of all birds.
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 sets P = {a} and B = {{a}} are equal.
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[a \subset A\]
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[\left\{ 1 \right\} \in A\]
Write down all possible subsets of each of the following set:
\[\left\{ \phi \right\}\]
Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second set. Then, the values of m and n are:
Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second. The values of m and n are respectively
If A and B are two finite sets, then n(A) + n(B) is equal to ______.
If A and B are finite sets such that A ⊂ B, then n (A ∪ B) = ______.
