English

Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine is A × B = B × A? - Mathematics

Advertisements
Advertisements

Question

Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine is A × B = B × A?

Sum

Solution

Since A = {1, 2, 3, 4} and B = {5, 7, 9}.

Therefore, No, A × B ≠ B × A.

Since A × B and B × A do not have exactly the same ordered pairs.

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Relations and Functions - Solved Examples [Page 22]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 2 Relations and Functions
Solved Examples | Q 1.(iii) | Page 22

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.


State whether the following statement is true or false. If the statement is false, rewrite the given statement correctly.

If A = {1, 2}, B = {3, 4}, then A × (B ∩ Φ) = Φ.


Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that A × (B ∩ C) = (A × B) ∩ (A × C)


The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0, 1). Find the set A and the remaining elements of A × A.


If A and B are two set having 3 elements in common. If n(A) = 5, n(B) = 4, find n(A × B) and n[(A × B) ∩ (B × A)].


Let A and B be two sets. Show that the sets A × B and B × A have elements in common iff the sets A and B have an elements in common. 


Let A = {1, 2, 3, 4} and R = {(ab) : a ∈ Ab ∈ Aa divides b}. Write R explicitly. 


If A = {1, 2, 3}, B = {4}, C = {5}, then verify that:

(iii) A × (B − C) = (A × B) − (A × C)


If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find

(ii) (A × B) ∩ (A × C)


If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find

(iii) A × (B ∪ C)


Prove that:

(i)  (A ∪ B) × C = (A × C) ∪ (B × C)

(ii) (A ∩ B) × C = (A × C) ∩ (B×C)

 

Find the domain of the real valued function of real variable: 

(ii)  \[f\left( x \right) = \frac{1}{x - 7}\]

 


Find the domain of the real valued function of real variable: 

(iii) \[f\left( x \right) = \frac{3x - 2}{x + 1}\]

 


Find the domain of the real valued function of real variable:

(iii) \[f\left( x \right) = \sqrt{9 - x^2}\]

 


Find the domain of the real valued function of real variable:

(iv)  \[f\left( x \right) = \frac{\sqrt{x - 2}}{3 - x}\]

 


Find the domain and range of the real valued function:

(ii) \[f\left( x \right) = \frac{ax - b}{cx - d}\]

 

 


Find the domain and range of the real valued function:

(v) \[f\left( x \right) = \frac{x - 2}{2 - x}\]


Find the domain and range of the real valued function:

(vi) \[f\left( x \right) = \left| x - 1 \right|\] 

 


Find the domain and range of the real valued function:

(x)  \[f\left( x \right) = \sqrt{x^2 - 16}\]


Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine B × A


Let A = {–1, 2, 3} and B = {1, 3}. Determine A × B


Let A = {–1, 2, 3} and B = {1, 3}. Determine B × A


State True or False for the following statement.

If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, then (A × B) ∪ (A × C) = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}.


State True or False for the following statement.

If A × B = {(a, x), (a, y), (b, x), (b, y)}, then A = {a, b}, B = {x, y}


The number of elements in the set {x ∈ R: (|x| –3)|x + 4| = 6} is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×