Let S- 1-2-3-n and A -a- b - - 1 - a- b - n - S - S- A subset B of A is said to be a good subset if x- x - B for every x - S- Then the number of good subsets of A is

The correct option is C 2^n(n 1) The number of element in A = n×n #160;The number of element of A having #160; (x,x) for all x∈ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Fundamental Principle of Counting

Let S= 1,2,...

Question

Let $S = {1, 2, 3, . . . . . . . n}$ and $A = {(a, b) | 1 \geq a, b \geq n} = S \times S$ . A subset $B$ of $A$ is said to be a good subset if $(x, x) \in B$ for every $x \in S .$ Then the number of good subsets of $A$ is

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2^{n}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2^{n (n - 1)}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2^{n^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $2^{n (n - 1)}$
The number of element in $A$ = $n \times n$
The number of element of A having $(x, x)$ for all $x \in S$ = $n$
Total remaining element = $(n \times n) - n$
Since Subset $B$ must have $(x, x)$ for all $x \in S$ = $n$ so it may have any number of remaining element.
Number of ways of selecting elements from remaining element = $2^{(n \times n) - n}$

Suggest Corrections

Similar questions

Q. Let

S = {1, 2, 3, \dots, n}

and

A = {(a, b) | 1 \leq a, b \leq n} = S \times S

. A subset

B

A

is said to be a good subset if

(x, x) \in B

for every

x \in S

. Then the number of good subsets of

A

A subset S of the set of numbers {2, 3, 4, 5, 6, 7, 8, 9, 10} is said to be good if it has exactly 4 elements and their greatest common divisor is 1. Let ‘n’ be the number of good subsets. Then the units digit of ‘n’ is___

Q. Assertion :A set

X

contains

n

elements. Two subsets

A

and

B

X

are chosen at random. The probability that

A

and

B

have same number of elements is

\frac{1.3.5... (2 n - 1)}{2^{n} (n!)}

. Reason:

{(^{n} C_{0})}^{2} + {(^{n} C_{1})}^{2} + . . . + {(^{n} C_{n})}^{2} = \frac{2^{n} (1.3.5... (2 n - 1))}{n!}

Q. If X is a finite set. Let

P (X)

denote the set of all subsets of X and let

n (X)

denote the number of elements in X. If for two finite subsets

A, B, n (P (A)) = n (P (B)) + 15

then

n (B) =

____,

n (A) =

_____

Q. If X is a finite set. Let P(X) denote the set of all subsets of X and let n(X) denote the number of elements in X. If for two finite subsets A, B, n(P(A)) = n(P(B)) + 15 then n(B) = and n(A) =

Join BYJU'S Learning Program

Let S={1,2,3,.......n} and A={(a,b)|1≥a,b≥n}=S×S. A subset B of A is said to be a good subset if (x,x)∈B for every x∈S. Then the number of good subsets of A is

Let $S = {1, 2, 3, . . . . . . . n}$ and $A = {(a, b) | 1 \geq a, b \geq n} = S \times S$ . A subset $B$ of $A$ is said to be a good subset if $(x, x) \in B$ for every $x \in S .$ Then the number of good subsets of $A$ is