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Relations And Functions

Question
CBSEENMA11013413
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Find A A B for the following pairs of sets :

WiredFaculty

Solution
space space space space space space space space space straight A space increment space straight B space equals space left parenthesis straight A space minus space straight B right parenthesis space union space left parenthesis straight B space minus space straight A right parenthesis
(a)     A = {a, e, i, o, u},  B = {a, b, c}
rightwards double arrow A - B { a, e, i, o, u}
Also, B - A = {b, c}
Hence,  space space space space straight A increment space straight B space equals space left parenthesis straight A minus straight B right parenthesis space union space left parenthesis straight B minus straight A right parenthesis space equals left curly bracket straight a comma space straight e comma space straight i comma space straight o comma space straight u right curly bracket space union space left curly bracket straight b comma space straight c right curly bracket space equals space left curly bracket space straight a comma space straight e comma space straight i comma space straight o comma space straight u comma space straight b comma space straight c right curly bracket
(b)      A = {1, 3, 5}, B = {1, 2, 3}
          A - B = {5}
          B - A = {2}
Hence,  WiredFaculty
(c)   space space space space space space space space space space straight A space equals space left curly bracket straight x space colon space straight x element of space straight N comma space 1 space less than space straight x space less or equal than 6 right curly bracket space space space space space space space space rightwards double arrow space space space space space space space straight A space equals space left curly bracket 2 comma space 3 comma space 4 comma space 5 comma space 6 right curly bracket
          WiredFaculty
               A - B = {2, 3, 4, 5}
      
               B - A = {7, 8, 9, 10}
Hence,  space space space space space space space space space space space straight A space increment space straight B space equals space left curly bracket space straight A space minus space straight B right curly bracket space union space left parenthesis straight B space minus straight A right curly bracket space equals space left curly bracket 2 comma space 3 comma space 4 comma space 5 right curly bracket space union space left curly bracket 7 comma space 8 comma space 9 comma space 10 right curly bracket
                    =  {2, 3, 4, 5, 7, 8, 9, 10}
(d)     space space space space space space straight A space equals space left curly bracket 1 comma space 2 comma space 3 right curly bracket comma space space straight B space equals space straight ϕ

∴  A - B = {1, 2, 3}
    space space space space space space straight B minus straight A equals straight ϕ
space space space space space space space space space space space straight A space increment space straight B space equals space left parenthesis straight A minus straight B right parenthesis space union space left parenthesis straight B minus straight A right parenthesis space equals space left curly bracket 1 comma space 2 comma space 3 right curly bracket space union space straight ϕ space equals space left curly bracket 1 comma space 2 comma space 3 right curly bracket
Hence,  space space space space space space space space space space space space space space space space straight A space increment space straight B space equals space left curly bracket 1 comma space 2 comma space 3 right parenthesis space equals space straight A

Some More Questions From Relations and Functions Chapter

Collection of natural numbers between 100 and 200 (both inclusive).

Collection of all odd integers.

Collection of all divisors of 42.

Collection of beautiful girls in India.

Fill in the blanks in the following table:

Numbers

Closed under
 

Addition

Subtraction

Multiplication

Division

Rational numbers

Yes

Yes

  

No

Integers

  

Yes

  

No

Whole numbers

...

  

Yes

  

Natural numbers

  

No

    
 

i9 + i19

3(7 + i7) + i(7 + i7)

Express each of the complex number given in the  form of  a + ib.

(1 - i) - (-1 + i6)

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