हिंदी

Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. If x ∈ A and A ∈ B, then x ∈ B - Mathematics

Advertisements
Advertisements

प्रश्न

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

If x ∈ A and A ∈ B, then x ∈ B

विकल्प

  • True

  • False

MCQ
सत्य या असत्य

उत्तर

This statement is False.

Explanation:

Let A = {1}, B = {{1}, 2}. Now, 1 ∈ A, A ∈ B, but 1 ∉ is the set B because 1 is not in B.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Sets - Miscellaneous Exercise [पृष्ठ २६]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
अध्याय 1 Sets
Miscellaneous Exercise | Q 2.1 | पृष्ठ २६

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

{a} ∈ (a, b, c)


Write down all the subsets of the following set:

{a}


Write the following as intervals: {x : x ∈ R, 3 ≤ x ≤ 4}


Write the following interval in set-builder form:

(6, 12]


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

If x ∈ A and A ⊄ B, then x ∈ B


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 x ∉ B, then x ∉ A


If a set contains n elements, then write the number of elements in its power set. 


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


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


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 \[n \left( A \cap B \right)\] 


The number of subsets of a set containing n elements is 


If A = |1, 2, 3, 4, 5|, then the number of proper subsets of A is 


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 equilateral triangle in a plane} _____ {x : x is a triangle in the same plane}


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

{1, 2, 5} ⊂ A


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

Φ ∈ A


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

Φ ⊂ A


Write down all the subsets of the following set:

{1, 2, 3}


Write down all the subsets of the following set:

Φ


Write the following interval in Set-Builder form:

(– 3, 0)


Given that N = {1, 2, 3, ..., 100}, then write the subset B of N, whose element are represented by x + 2, where x ∈ N.


Given that N = {1, 2, 3, ... , 100}. Then write the subset of N whose elements are even 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 X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by n – 1


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


State True or False for the following statement.

If A is any set, then A ⊂ A.


State True or False for the following statement.

Q ∪ Z = Q, where Q is the set of rational numbers and Z is the set of integers.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×