हिंदी

If a = {1, 2} and B = {1, 3}, Find a × B and B × A. - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

Given:
A = {1, 2} and B = {1, 3}
Now,
A × B = {(1, 1), (1, 3), (2, 1), (2, 3)}
B × A = {(1, 1), (1, 2), (3, 1), (3, 2)}

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Relations - Exercise 2.1 [पृष्ठ ८]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 2 Relations
Exercise 2.1 | Q 5 | पृष्ठ ८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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


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


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.

 

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


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)


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

(ii) (A × B) ∩ (A × C)


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

(iv) (A × B) ∪ (A × 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: 

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

 


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:

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

 


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:

(i) \[f\left( x \right) = \frac{ax + b}{bx - a}\]

 


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:

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

 


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).

 
 
 

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


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


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


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


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


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)}


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×