Advertisements
Advertisements
Question
The set {x ∈ R : 1 ≤ x < 2} can be written as ______.
Advertisements
Solution
The set {x ∈ R : 1 ≤ x < 2} can be written as [1, 2).
Explanation:
Given: {x ∈ R: 1 ≤ x < 2}
The symbol ∈ R means the set contains all continuous real values between 1 and 2, which requires interval notation rather than roster form.
The condition 1 ≤ x means 1 is included, represented by a closed square bracket: [1
The condition x < 2 means 2 is excluded, represented by an open parenthesis: 2)
Combining these gives the interval [1, 2).
APPEARS IN
RELATED QUESTIONS
Identify whether the following is set or not? Justify your answer.
A team of eleven best-cricket batsmen of the world.
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
5 _____ A
Write the following set in roster form:
A = {x : x is an integer and –3 ≤ x < 7}
Write the following set in roster form:
B = {x : x is a natural number less than 6}
Write the following set in roster form:
C = {x : x is a two-digit natural number such that the sum of its digits is 8}
Write the following set in the set-builder form:
{3, 6, 9, 12}
Describe the following sets in Roster form:
{x : x is a letter before e in the English alphabet}
Describe the following sets in Roster form:
The set of all letters in the word 'Better'.
Describe the following sets in set-builder form:
E = {0}
Describe the following sets in set-builder form:
{2, 4, 6, 8 .....}
List all the elements of the following sets:
\[A = \left\{ x: x^2 \leq 10, x \in Z \right\}\]
Write the set of all vowels in the English alphabet which precede q.
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ a, b \right\} \subset \left\{ a, \left\{ b, c \right\} \right\}\]
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\phi \subset \left\{ a, b, c \right\}\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\left\{ c, d \right\} \subset A\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\left\{ c, d \right\} \in A\]
Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false:
\[\left\{ 6, 7, 8 \right\} \in A\]
Write down all possible subsets of each of the following set:
{a, b, c},
Write down all possible subsets of each of the following set:
{1, {1}},
Write down all possible proper subsets each of the following set:
{1, 2, 3}
If A is any set, prove that: \[A \subseteq \phi \Leftrightarrow A = \phi .\]
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, = {2, 4, 6, 8} and C = {3, 4, 5, 6}.
Find \[\left( A \cap C \right)'\]
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
0 ____ A
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
10 _____ A
Describe the following set in Roster form
C = {x/x = 2n + 1, n ∈ N}
Describe the following set in Set-Builder form
`{1/2, 2/5, 3/10, 4/17, 5/26, 6/37, 7/50}`
Describe the following set in Set-Builder form
{0, –1, 2, –3, 4, –5, 6, ...}
If A = {x/6x2 + x – 15 = 0}, B = {x/2x2 – 5x – 3 = 0}, C = {x/2x2 – x – 3 = 0} then find (A ∩ B ∩ C)
From amongst 2000 literate individuals of a town, 70% read Marathi newspapers, 50% read English newspapers and 32.5% read both Marathi and English newspapers. Find the number of individuals who read neither Marathi and English newspaper
Select the correct answer from given alternative.
In a city 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then, persons travelling by car or bus are
Answer the following:
In a survey of 425 students in a school, it was found that 115 drink apple juice, 160 drink orange juice, and 80 drink both apple as well as orange juice. How many drinks neither apple juice nor orange juice?
State which of the following statement are true and which are false. Justify your answer.
28 ∈ {y | the sum of the all positive factors of y is 2y}
State which of the following statement are true and which are false. Justify your answer.
7,747 ∈ {t | t is a multiple of 37}
In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows:
French = 17, English = 13, Sanskrit = 15 French and English = 09, English and Sanskrit = 4 French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study French and English but not Sanskrit
Let R be set of points inside a rectangle of sides a and b (a, b > 1) with two sides along the positive direction of x-axis and y-axis. Then ______.
In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Then, the number of students who play neither is ______.
A survey shows that 63% of the people watch a News Channel whereas 76% watch another channel. If x% of the people watch both channel, then ______.
