English

State whether the following statement is true or false. If the statement is false, rewrite the given statement correctly. If A and B are non-empty sets, - Mathematics

Advertisements
Advertisements

Question

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

If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ A and y ∈ B.

Options

  • True

  • False

MCQ
True or False

Solution

This statement is True.

Explanation:

Because A × B is the non-empty set of ordered pairs (x, y) such that X ∈ A and Y ∈ B.

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Relations and Functions - Exercise 2.1 [Page 33]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 2 Relations and Functions
Exercise 2.1 | Q 4.2 | Page 33

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 P = {m, n} and Q = {n, m}, then P × Q = {(m, n), (n, m)}.


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.


If A = {–1, 1}, find A × A × A.


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)


Let A and B be two sets such that n(A) = 3 and n (B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y and z are distinct elements.


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 = {1, 2, 3} and B = {2, 4}, what are A × BB × AA × AB × B and (A × B) ∩ (B × 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, 1}, find A × A × A.


State whether of  the statement is true or false. If the statement is false, re-write the given statement correctly:

If P = {m, n} and Q = {n, m}, then P × Q = {(m, n), (n, m)}


If A = {1, 2}, from the set A × A × A.


If A = {2, 3}, B = {4, 5}, C ={5, 6}, find A × (B ∪ C), A × (B ∩ C), (A × B) ∪ (A × C).

 

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

(iii) A × (B − C) = (A × B) − (A × C)


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

(i) A × C ⊂ B × D


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

(i) A × (B ∩ C)


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

(iii) A × (B ∪ C)


If A × B ⊆ C × D and A × B ≠ ϕ, prove that A ⊆ C and B ⊆ D.

 

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

(i)  \[f\left( x \right) = \frac{1}{x}\]

 


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

(iv)  \[f\left( x \right) = \frac{2x + 1}{x^2 - 9}\]

 


Find the domain and range of the real valued function:

(iii)  \[f\left( x \right) = \sqrt{x - 1}\]

 


Find f + gf − gcf (c ∈ R, c ≠ 0), fg, \[\frac{1}{f}\text{  and } \frac{f}{g}\] in :

(a) If f(x) = x3 + 1 and g(x) = x + 1


Find f + gf − gcf (c ∈ R, c ≠ 0), fg, \[\frac{1}{f}\text{  and } \frac{f}{g}\] in : 

(b) If \[f\left( x \right) = \sqrt{x - 1}\]  and  \[g\left( x \right) = \sqrt{x + 1}\]

 


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


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


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


If A = {2, 4, 6, 9} and B = {4, 6, 18, 27, 54}, a ∈ A, b ∈ B, find the set of ordered pairs such that 'a' is factor of 'b' and a < b.


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


If A = {x : x ∈ W, x < 2} B = {x : x ∈ N, 1 < x < 5} C = {3, 5} find A × (B ∪ C)


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}


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×