हिंदी

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

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 A ⊂ B and B ∈ C, then A ∈ C

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

This statement is False.

Explanation:

Let A = {1}, B = {1, 2} and C = {{1, 2}, 3}

The elements of set A are in set B.

∴ A ∈ B

The elements {1, 2} are in the set C” B ∈ C

But A = {1} is not in the set C.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Sets - Miscellaneous Exercise [पृष्ठ २१]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
अध्याय 1 Sets
Miscellaneous Exercise | Q 2. (ii) | पृष्ठ २१

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

{a, e} ⊂ {x : x is a vowel in the English alphabet}


Write the following as interval:

{x : x ∈ R, – 4 < x ≤ 6}


Write the following as intervals: {x : x ∈ R, 0 ≤ x < 7}


Write the following interval in set-builder form:

(6, 12]


Decide, among the following sets, which sets are subsets of one and another:

A = {x : x ∈ R and x satisfy x2 – 8x + 12 = 0},

B = {2, 4, 6}, C = {2, 4, 6, 8, …}, D = {6}.


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


Let A and B be two sets having 3 and 6 elements respectively. Write the minimum number of elements that \[A \cup B\] 


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


If \[A = \left\{ \left( x, y \right) : y = e^x , x \in R \right\} and B = \left\{ \left( x, y \right) : y = e^{- x} , x \in R \right\}\]write\[A \cap B\] 


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 \[n \left( A \cap B \right)\] 


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


In set-builder method the null set is represented by


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

{x : x is a circle in the plane} _____ {x : x is a circle in the same plane with radius 1 unit}


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

{x : x is a triangle in a plane} _____ {x : x is a rectangle in the plane}


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 ∈ 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, 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


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:

{a, b}


Write down all the subsets of the following set:

Φ


Write the following interval in Set-Builder form:

(– 3, 0)


State true or false for the following statement given below:

Let R and S be the sets defined as follows:
R = {x ∈ Z | x is divisible by 2}
S = {y ∈ Z | y is divisible by 3}
then R ∩ S = φ


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


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 ______.


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.


State True or False for the following statement.

The sets {1, 2, 3, 4} and {3, 4, 5, 6} are equal.


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×