मराठी

If N(A) = 3, N(B) = 4, Then Write N(A × a × B).

Advertisements
Advertisements

प्रश्न

If n(A) = 3, n(B) = 4, then write n(A × A × B).

 
Advertisements

उत्तर

Given:
n(A) = 3 and n(B) = 4
Now, we have:
n(A × A × B) =  \[n\left( A \times A \right) \times n\left( B \right) = 3 \times 3 \times 4 = 36\]

 

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Relations - Exercise 2.4 [पृष्ठ २४]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 2 Relations
Exercise 2.4 | Q 2 | पृष्ठ २४

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

The given figure shows a relationship between the sets P and Q. Write this relation

  1. in set-builder form.
  2. in roster form.

What is its domain and range?


Let A = [1, 2] and B = [3, 4]. Find the total number of relation from A into B.

 

Determine the domain and range of the relation R defined by

(ii) R = {(x, x3) : x is a prime number less than 10}

 

Let R be a relation from N to N defined by R = {(a, b) : a, b ∈ N and a = b2}. Is the statement true?

(a, b) ∈ R and (b, c) ∈ R implies (a, c) ∈ R

Justify your answer in case.


Let A = [1, 2, 3, ......., 14]. Define a relation on a set A by
R = {(x, y) : 3x − y = 0, where x, y ∈ A}.
Depict this relationship using an arrow diagram. Write down its domain, co-domain and range.


Define a relation R on the set N of natural number by R = {(x, y) : y = x + 5, x is a natural number less than 4, x, y ∈ N}. Depict this relationship using (i) roster form (ii) an arrow diagram. Write down the domain and range or R.


Let R be a relation on N × N defined by
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N
Show that:
(i) (a, b) R (a, b) for all (a, b) ∈ N × N


Let R be a relation on N × N defined by
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N
Show that:

(ii) (a, b) R (c, d) ⇒ (c, d) R (a, b) for all (a, b), (c, d) ∈ N × N

 

 


If R = {(x, y) : x, y ∈ Z, x2 + y2 ≤ 4} is a relation defined on the set Z of integers, then write domain of R.


Let A = [1, 2, 3, 5], B = [4, 6, 9] and R be a relation from A to B defined by R = {(x, y) : x − yis odd}. Write R in roster form. 


A relation ϕ from C to R is defined by x ϕ y ⇔ |x| = y. Which one is correct?

 

R is a relation from [11, 12, 13] to [8, 10, 12] defined by y = x − 3. Then, R−1 is


If R is a relation from a finite set A having m elements of a finite set B having n elements, then the number of relations from A to B is


Write the relation in the Roster Form. State its domain and range

R6 = {(a, b)/a ∈ N, a < 6 and b = 4}


Write the relation in the Roster Form. State its domain and range

R8 = {(a, b)/b = a + 2, a ∈ z, 0 < a < 5}


Identify which of if the following relations are reflexive, symmetric, and transitive.

Relation Reflexive Symmetric Transitive
R = {(a, b) : a, b ∈ Z, a – b is an integer}      
R = {(a, b) : a, b ∈ N, a + b is even} √ √ x
R = {(a, b) : a, b ∈ N, a divides b}      
R = {(a, b) : a, b ∈ N, a2 – 4ab + 3b2 = 0}      
R = {(a, b) : a is sister of b and a, b ∈ G = Set of girls}      
R = {(a, b) : Line a is perpendicular to line b in a plane}      
R = {(a, b) : a, b ∈ R, a < b}      
R = {(a, b) : a, b ∈ R, a ≤ b3}      

Select the correct answer from given alternative.

The relation ">" in the set of N (Natural number) is


Answer the following:

Find R : A → A when A = {1, 2, 3, 4} such that R = (a, b)/a − b = 10}


Answer the following:

R = {1, 2, 3} → {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} Check if R is reflexive


Answer the following:

Check if R : Z → Z, R = {(a, b)/2 divides a – b} is equivalence relation.


Answer the following:

Show that the following is an equivalence relation

R in A is set of all books. given by R = {(x, y)/x and y have same number of pages}


Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R1 = {(2, 1), (7, 1)}


A Relation R is given by the set `{(x, y)/y = x + 3, x ∈ {0, 1, 2, 3, 4, 5}}`. Determine its domain and range


Represent the given relation by
(a) an arrow diagram
(b) a graph and
(c) a set in roster form, wherever possible

{(x, y) | x = 2y, x ∈ {2, 3, 4, 5}, y ∈ {1, 2, 3, 4}


Multiple Choice Question :

Let n(A) = m and n(B) = n then the total number of non-empty relation that can be defined from A to B is ________.


Find the domain of the function f(x) = `sqrt(1 + sqrt(1 - sqrt(1 - x^2)`


Let A = {a, b, c} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it equivalence


In the set Z of integers, define mRn if m − n is divisible by 7. Prove that R is an equivalence relation


Choose the correct alternative:

Let R be the set of all real numbers. Consider the following subsets of the plane R × R: S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x − y is an integer} Then which of the following is true?


If R2 = {(x, y) | x and y are integers and x2 + y2 = 64} is a relation. Then find R2.


Is the given relation a function? Give reasons for your answer.

h = {(4, 6), (3, 9), (– 11, 6), (3, 11)}


Is the given relation a function? Give reasons for your answer.

g = `"n", 1/"n" |"n"` is a positive integer


Let n(A) = m, and n(B) = n. Then the total number of non-empty relations that can be defined from A to B is ______.


If R = {(x, y): x, y ∈ Z, x2 + 3y2 ≤ 8} is a relation on the set of integers Z, then the domain of R–1 is ______.


A relation on the set A = {x : |x| < 3, x ∈ Z}, where Z is the set of integers is defined by R = {(x, y) : y = |x| ≠ –1}. Then the number of elements in the power set of R is ______.


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 function from A to B

Justify your answer in case.


Which statement about images in a function is correct?


Find \(x\) and \(y\) if \((x+3,2)=(4,y-3)\).


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×