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Relations And Functions

Question
CBSEENMA11013380
Wired Faculty App

Which of the following pairs of sets are disjoint?

(i) {1, 2, 3, 4} and {x : x is a natural number and 4 ≤ x ≤ 6 }

(ii) { a, e, i, o, u } and { c, d, e, f }

(iii) {x : x is an even integer } and {x : x is an odd integer}

Solution

(i)  A = {1, 2, 3, 4},    
 
        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 B space equals space space space space space space space space space left curly bracket space straight x thin space space colon space straight x space element of space straight N comma space space 4 space less or equal than space straight x space less or equal than space right curly bracket space equals space left curly bracket 4 comma space 5 comma space 6 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 rightwards double arrow space space straight A space intersection space straight B space equals space left curly bracket 1 comma space 2 comma space 3 comma space 4 right curly bracket space intersection space left curly bracket 4 comma space 5 comma space 6 right curly bracket space equals space left curly bracket 4 right curly bracket space equals straight ϕ
Hence, A and B are not disjoint sets.

(ii)               A = { a, e, i, o, u },   B =  { c, d, e, f }
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∴   A and B are not disjoint sets.

(iii)    A   =   {x : x is an even integer}
              = {........, -6, -4, -2, 0, 2, 4, 6, 8, 10, ................}
         B = {and {x : x is an odd integer} = {........., -5, -3, -1, 1, 3, 5, 7, .............}
space space space space space space space space space space rightwards double arrow space space space space space straight A space intersection space straight B space equals space left curly bracket space space space right curly bracket space equals space straight ϕ
Hence, A and B are disjoint sets. 

 

Some More Questions From Relations and Functions Chapter

Collection of all the months of a year beginning with the letter J.

A team of eleven best cricket batsmen in the world. 

Collection of ten most talented writers of India.

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

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