Advertisements
Advertisements
प्रश्न
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 ______.
विकल्प
4, 7
7, 4
4, 4
7, 7
उत्तर
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 7, 4.
Explanation:
Number of subsets of a given set having m element = 2m and the number of subsets of set containing n elements = 2n
As per the given condition, we have
2m – 2n = 112
⇒ 2n (2m – n – 1) = 112
⇒ 2n .(2m – n – 1) = 24 .7
⇒ 2n = 24 and 2m – n – 1 = 7
⇒ n = 4 and 2m – n = 1 + 7 = 8 = 23
⇒ n = 4 and m – n = 3
⇒ m – 4 = 3
⇒ m = 7
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 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?
Set of concentric circles in a plane
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 ∈ 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 statements are true? Give reason to support your answer.
Every subset of a finite set is finite
State whether the following statements are true or false:
\[1 \in \left\{ 1, 2, 3 \right\}\]
State whether the following statements are true or false:
\[a \subset {b, c, a}\]
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 real numbers is contained in the set of all complex numbers.
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?
\[\left\{ a, b, e \right\} \subset A\]
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 is a finite set containing n element, then number of subsets of A is ______.
If A and B are finite sets such that A ⊂ B, then n (A ∪ B) = ______.
