Relations and Functions class 11 and 12th

 

 

  1)  2) Types of Relations 3) Identity Relation 4) Reflexive Relation  Even if some elements are related to more than 1 element, it is compulsory for those elements to be related to themselves for the relation to be Reflexive. For example in the below example '1'  R ' 1' and also '1' R '2' (here R means Relates to). 5) Total Number of Reflexive Relations of a Finite set Formula and Derivations Here the n elements are compulsory but the rest of the elements (n²  - n) have 2 possibilities, they can either come or not come. Therefore the 2 possibilities comes n ²  - n ( remaining elements)  times.  Hence the formula 2 ^  n ²  - n . 6) Symmetric Relations Note: null relations are also symmetric relations since the definition says if aRb then bRa should compulsorily be there but if aRb is not in the relation then bRa need not be in the relation too, and that is exactly the case with null relations, i.e., R = {}. 7)  Total Number of Sy...

  1)  2)  3) 4)  5)  6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19)