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so what is lower bound the definition goes as the smallest index yes the smallest index such that the number at that index is greater than equal to the given number letamp;#39;s take an example so this is a sorted array again the array has to be sorted for lower bound to be implemented imagine I give you X as eight if I give you X as 8 I can say the smallest index is 3 no itamp;#39;s five no S8 yes why because 8 is greater than equal to 8 thatamp;#39;s why this is the first index where you get a number that is greater than equal to correct so what is the index if I have to write down the index 0 1 2 3 4 so the low bound will go as 2. quite simple what if x is nine in this case letamp;#39;s see N3 N5 can 8 15 yes 15 can be because 15 is greater than equal to 9 because X is nine so thereby the index will go as three perfect what if x is letamp;#39;s say 16. in that case is it no is it no is it no is it no yes this is 19 greater than equal to 16 so thereby the lower bound will be 4 i