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. The values of m and n are respectively
पर्याय
(a) 4, 7
(b) 7, 4
(c) 4, 4
(c) 4, 4
उत्तर
We know that if a set X contains k elements, then the number of subsets of X are 2k.
It is given that the number of subsets of a set containing m elements is 112 more than the number of subsets of set containing n elements.
\[\therefore 2^m - 2^n = 112\]
\[ \Rightarrow 2^n \left( 2^{m - n} - 1 \right) = 2 \times 2 \times 2 \times 2 \times 7\]
\[ \Rightarrow 2^n \left( 2^{m - n} - 1 \right) = 2^4 \left( 2^3 - 1 \right)\]
\[ \Rightarrow n = 4 \text{ and } m - n = 3\]
\[ \therefore m - 4 = 3\]
\[ \Rightarrow m = 7\]
Thus, the values of m and n are 7 and 4, respectively.
Hence, the correct answer is option (b).
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 positive integers greater than 100.
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 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 ∈ 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.
(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 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, b, c} and {1, 2, 3} are equivalent sets
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:
\[1 \in \left\{ 1, 2, 3 \right\}\]
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 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 = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\left\{ a, b, e \right\} \subset A\]
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:
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 respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively 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 set. The values of m and n are, respectively ______.
