The values of remainder r ,when a positive integer a is divided by 3,are 0 and 1 only. Is this statement true or false? Justify your answer.
(Class 10 Maths Sample Question Paper)
(Class 10 Maths Sample Question Paper)
Add an Answer
More Questions From This User See All
Answers & Comments
Verified answer
SOLUTION:The given statement the values of remainder r ,when a positive integer a is divided by 3,are 0 and 1 only is FALSE. According to Euclid's division Lemma, a = b q+ r
Here, b = 3
a = 3 q + r,
Where 0 ≤ r < 3 and r is an integer.
Therefore , the values of r can be zero ( 0 ) , one ( 1 ) or two ( 2 ).
HOPE THIS WILL HELP YOU....
Let a be the positive integer and b = 3 be the divisor then there exist ,
a = bq + r , where 0≤r< b ...... ( 1 )
Here ,
statement says that -
"When a which is an positive integer divided by three then remainder will be 0 or 1 only"
But we know from ( 1 ) that
remainder can be , ➱ 0 , 1 , 2
Hence this statement is proven to be false
Hope this would help you !!