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List all the elements of the following set:
D = {x : x is a letter in the word “LOYAL”}
Concept: undefined >> undefined
List all the elements of the following set:
E = {x : x is a month of a year not having 31 days}
Concept: undefined >> undefined
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List all the elements of the following set:
F = {x : x is a consonant in the English alphabet which precedes k}.
Concept: undefined >> undefined
Match each of the set on the left in the roster form with the same set on the right described in set-builder form:
| (i) | {1, 2, 3, 6} | (a) | {x : x is a prime number and a divisor of 6} |
| (ii) | {2, 3} | (b) | {x : x is an odd natural number less than 10} |
| (iii) | {M, A, T, H, E, I, C, S} | (c) | {x : x is natural number and divisor of 6} |
| (iv) | {1, 3, 5, 7, 9} | (d) | {x : x is a letter of the word MATHEMATICS} |
Concept: undefined >> undefined
Let A = {1, 2, 3, …, 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range.
Concept: undefined >> undefined
Define a relation R on the set N of natural numbers by R = {(x, y): y = x + 5, x is a natural number less than 4; x, y ∈ N}. Depict this relationship using roster form. Write down the domain and the range.
Concept: undefined >> undefined
A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.
Concept: undefined >> undefined
The given figure shows a relationship between the sets P and Q. Write this relation
- in set-builder form.
- in roster form.
What is its domain and range?
Concept: undefined >> undefined
Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a, b ∈ A, b is exactly divisible by a}.
- Write R in roster form
- Find the domain of R
- Find the range of R.
Concept: undefined >> undefined
Determine the domain and range of the relation R defined by R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}.
Concept: undefined >> undefined
Write the relation R = {(x, x3): x is a prime number less than 10} in roster form.
Concept: undefined >> undefined
Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.
Concept: undefined >> undefined
Let R be the relation on Z defined by R = {(a, b): a, b ∈ Z, a – b is an integer}. Find the domain and range of R.
Concept: undefined >> undefined
The relation f is defined by f(x) = `{(x^2,0<=x<=3),(3x,3<=x<=10):}`
The relation g is defined by g(x) = `{(x^2, 0 <= x <= 2),(3x,2<= x <= 10):}`
Show that f is a function and g is not a function.
Concept: undefined >> undefined
Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Is the following true?
f is a relation from A to B
Justify your answer in case.
Concept: undefined >> undefined
Which of the following collection are sets? Justify your answer:
The collection of all girls in your class.
Concept: undefined >> undefined
Which of the following collection is set? Justify your answer:
The collection of ten most talented writers of India.
Concept: undefined >> undefined
Which of the following collection are sets? Justify your answer:
The collection of difficult topics in mathematics.
Concept: undefined >> undefined
Which of the following collection are sets? Justify your answer:
A collection of novels written by Munshi Prem Chand.
Concept: undefined >> undefined
Which of the following collection are sets? Justify your answer:
The collection of all question in this chapter.
Concept: undefined >> undefined
