English

If a = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, Find(Iii) a × (B ∪ C) - Mathematics

Advertisements
Advertisements

Question

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

(iii) A × (B ∪ C)

Solution

Given:
A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}

(iii) A × (B ∪ C)
Now,
(B ∪ C) = {3, 4, 5, 6}
∴ A × (B ∪ 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)}

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Relations - Exercise 2.2 [Page 12]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 2 Relations
Exercise 2.2 | Q 5.3 | Page 12

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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


If A = {–1, 1}, find A × A × A.


If A × B = {(a, x), (a, y), (b, x), (b, y)}. Find A and B.


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 = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.


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.


If A = {1, 2} and B = {1, 3}, find A × B and 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:

(iii) 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:

(i) A × C ⊂ B × D


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

(ii) (A × B) ∩ (A × 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: 

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

 


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

(ii) \[f\left( x \right) = \frac{1}{\sqrt{x^2 - 1}}\]

 


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:

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


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


If f(x) be defined on [−2, 2] and is given by \[f\left( x \right) = \begin{cases}- 1, & - 2 \leq x \leq 0 \\ x - 1, & 0 < x \leq 2\end{cases}\]  and g(x)

\[= f\left( \left| x \right| \right) + \left| f\left( x \right) \right|\] , find g(x).

 
 
 

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 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 × B


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


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


If P = {x : x < 3, x ∈ N}, Q = {x : x ≤ 2, x ∈ W}. Find (P ∪ Q) × (P ∩ Q), where W is the set of whole numbers.


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


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 P = {1, 2}, then P × P × P = {(1, 1, 1), (2, 2, 2), (1, 2, 2), (2, 1, 1)}


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×