Advertisements
Advertisements
प्रश्न
Which of the following statements are true? Give reason to support your answer.
(i) For any two sets A and B either \[A \subseteq B o\text{ or } B \subseteq A;\]
Advertisements
उत्तर
\[ \text{ False } \]
It is not necessary that for any two sets A & B, either A ⊆ B or B ⊆ A.
\[\text{ It is not satisfactory always } . \]
\[\text{ Let }: \]
A={1,2} & B={α,β,γ}
\[\text{ Here, neither } A \subseteq B n \text{ nor } B \subseteq A . \]
\[\]
\[\]
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, ... 99, 100}
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 circles passing through the origin (0, 0).
Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = Φ.
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 sets are finite and which are infinite?
{x ∈ Z : x < 5};
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
State whether the following statements are true or false:
\[a \subset {b, c, a}\]
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 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 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 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?
\[a \subset A\]
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?\[\left\{ 2 \left\{ 1 \right\} \right\} \not\subset A\]
Write down all possible subsets of each of the following set:
\[\left\{ \phi \right\}\]
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
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 ______.
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 ______.
If A and B are finite sets such that A ⊂ B, then n (A ∪ B) = ______.
