हिंदी

How Many Elements Has P(A), If a = φ? - Mathematics

Advertisements
Advertisements

प्रश्न

How many elements has P(A), if A = Φ?

योग
Advertisements

उत्तर

We know that if A is a set with m elements i.e., n(A) = m, then n[P(A)] = 2m.

If A = Φ, then n(A) = 0.

∴ n[P(A)] = 20 = 1

Hence, P(A) has one element.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Sets - Exercise 1.3 [पृष्ठ १३]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
अध्याय 1 Sets
Exercise 1.3 | Q 5 | पृष्ठ १३

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

{1, 2, 3} ⊂ {1, 3, 5}


{x : x is an even natural number less than 6} ⊂ {x : x is a natural number which divides 36}


Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?

{3, 4} ⊂ A


Write down all the subsets of the following set:

{a}


Write the following interval in set-builder form:

[–23, 5)


Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If A ⊂ B and B ∈ C, then A ∈ C


Write the number of elements in the power set of null set. 


If A = {x ∈ C : x2 = 1} and B = {x ∈ C : x4 = 1}, then write A − B and B − A


If A and B are two sets such that \[A \subset B\], then write B' − A' in terms of A and B.


Let A and B be two sets having 4 and 7 elements respectively. Then write the maximum number of elements that \[A \cup B\] can have. 


If A and B are two sets such that \[n \left( A \right) = 20, n \left( B \right) = 25\]\text{ and } \[n \left( A \cup B \right) = 40\], then write \[n \left( A \cap B \right)\] 


If A = {1, 3, 5, B} and B = {2, 4}, then 


Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:

{a, b, c} _____ {b, c, d}


Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:

{x : x is a student of Class XI of your school} ____ {x : x student of your school}


Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:

{x : x is an even natural number} _____ {x : x is an integer}


Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?

{{3, 4}} ⊂ A


Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?

1 ∈ A


Let A = { 1, 2, { 3, 4}, 5 }. The following statement is correct or incorrect and why?

1 ⊂ A


Write down all the subsets of the following set:

{a, b}


Write down all the subsets of the following set:

{1, 2, 3}


Write the following interval in Set-Builder form:

(– 3, 0)


Given that N = {1, 2, 3, ..., 100}, then write the subset A of N, whose element are odd numbers.


State true or false for the following statement given below:

Q ∩ R = Q, where Q is the set of rational numbers and R is the set of real numbers.


Given that N = {1, 2, 3, ... , 100}. Then write the subset of N whose element are perfect square numbers.


If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by 4n


If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by n + 6


If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.

a ∈ Y but a2 ∉ Y


If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.

a + 1 = 6, a ∈ Y


If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.

a is less than 6 and a ∈ Y


Suppose A1, A2, ..., A30 are thirty sets each having 5 elements and B1, B2, ..., Bn are n sets each with 3 elements, let \[\bigcup\limits_{i=1}^{30} A_{i} = \bigcup\limits_{j=1}^{n} B_{j}\] = and each element of S belongs to exactly 10 of the Ai’s and exactly 9 of the B,’S. then n is equal to ______.


If X = {8n – 7n – 1 | n ∈ N} and Y = {49n – 49 | n ∈ N}. Then ______.


State True or False for the following statement.

Given that M = {1, 2, 3, 4, 5, 6, 7, 8, 9} and if B = {1, 2, 3, 4, 5, 6, 7, 8, 9}, then B ⊄ M.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×