Q. 54.1( 60 Votes )

Show that every p

Answer :

Using Euclid’s divison lemma -

a = bq + r;


We want to show that any even integer is of the form '2q' and any odd integer is of the form'2q + 1'


So, we take the two integers a and 2.


When we divide a with 2, the possible values of remainder are 0 and 1, which means


a = 2q + 0 or a = 2q + 1


Also, 2q is always an even integer for any integral value of q and so 2q + 1 will always be an odd integer. ( 'even integer + 1' is always an odd integer)


when a is a positive even integer it will always be of the form 2q


And when a is positive odd integer it will always be of the form 2q + 1.


for every positive integer it is either odd or even.


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