English

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

Advertisements
Advertisements

Question

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

Solution

Given:
A = {1, 2}
Now,
A × A = {(1, 1), (1, 2), (2, 1), (2, 2)}
∴ A × A × A = {(1, 1, 1), (1, 1, 2), (1, 2, 1), (1, 2, 2), (2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2)}

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Relations - Exercise 2.1 [Page 8]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 2 Relations
Exercise 2.1 | Q 14 | Page 8

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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.


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.


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


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


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)}


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.

 

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

(i) A × (B ∪ C) = (A × B) ∪ (A × C)


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

(ii) 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


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: 

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

 


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

(v)  \[f\left( x \right) = \frac{x^2 + 2x + 1}{x^2 - 8x + 12}\]

 


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:

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

 


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:

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

 


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 f(x) = 2x + 5 and g(x) = x2 + x. Describe (i) f + g (ii) f − g (iii) fg (iv) f/g. Find the domain in each case.

 

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).

 
 
 

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×