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Relations And Functions

Question
CBSEENMA11013535
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Is it true that for any sets A and B, P ( A ) ∪ P ( B ) = P ( A ∪ B )? Justify your answer.

Solution

No,  Let    A = {1, 2}, B  = [2,3}
rightwards double arrow      space space space space space space space space space space space space straight A space union space straight B space space space equals space left curly bracket 1 comma space 2 comma space 3 right curly bracket
             WiredFaculty


            space space space space space space space space straight P left parenthesis bold B right parenthesis space equals space left curly bracket straight ϕ comma space left curly bracket 1 right curly bracket comma space left curly bracket 2 right curly bracket comma space left curly bracket 1 comma space 2 right curly bracket right curly bracket

∴     space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight P left parenthesis straight A right parenthesis space union space straight P left parenthesis straight B right parenthesis space equals space left curly bracket straight ϕ comma space left curly bracket 1 right curly bracket comma space left curly bracket 3 right curly bracket comma space left curly bracket 1 comma space 2 right curly bracket comma space left curly bracket 2 comma space 3 right curly bracket right curly bracket                                      ...(i)
                                space space space space space space space space space space space space straight A union straight B space equals space left curly bracket 1 comma space 2 comma space 3 right curly bracket

rightwards double arrow space      WiredFaculty       ...(ii)

From (i) and (ii), it is clear that uin genera,
space space space space space space space space space space space space space space space space space space space space space space space space straight P left parenthesis straight A right parenthesis union straight P left parenthesis straight B right parenthesis space not equal to space straight P left parenthesis straight A union straight B right parenthesis

Some More Questions From Relations and Functions Chapter

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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