Advertisements
Advertisements
Question
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.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
Since every integer is a rational number.
∴ Z ⊂ Q and Q ∪ Z = Q.
APPEARS IN
RELATED QUESTIONS
Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:
{2, 3, 4} _____ {1, 2, 3, 4, 5}
{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, –12 < x < –10}
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 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 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 x ∈ A and A ⊄ B, then x ∈ B
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.
Let A = {x : x ∈ N, x is a multiple of 3} and B = {x : x ∈ N and x is a multiple of 5}. Write \[A \cap B\]
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 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 \[n \left( A \cap B \right)\]
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 \[n \left( A \cup B \right)\]
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?
{1, 2, 5} ∈ 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
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.
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 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 – 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 is less than 6 and a ∈ Y
If X = {8n – 7n – 1 | n ∈ N} and Y = {49n – 49 | n ∈ N}. Then ______.
