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
Advertisements
उत्तर
This statement is False.
Explanation:
Let A = {3, 5, 7} and B = {3, 4, 6}
Now, 5 ∈ A and A ⊄ B
However, 5 ∉ B
APPEARS IN
संबंधित प्रश्न
{a, b} ⊄ {b, c, a}
{1, 2, 3} ⊂ {1, 3, 5}
Write down all the subsets of the following set:
{a}
Write the following as interval:
{x : x ∈ R, – 4 < x ≤ 6}
Write the following as intervals: {x: x ∈ R, –12 < x < –10}
Write the following as intervals: {x : x ∈ R, 0 ≤ x < 7}
Write the following as intervals: {x : x ∈ R, 3 ≤ x ≤ 4}
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}.
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
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
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
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.
Let A = {x : x ∈ N, x is a multiple of 3} and B = {x : x ∈ N and x is a multiple of 5}. Write \[A \cap B\]
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 \[n \left( A \right) = 115, n \left( B \right) = 326, n \left( A - B \right) = 47,\] then write \[n \left( A \cup B \right)\]
For any two sets A and B,\[A \cap \left( A \cup B \right) =\]
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 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?
{{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, 2, 3} ⊂ 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:
Φ
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 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 ∈ 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.
If A is any set, then A ⊂ A.
