Question

If b=3,then any integer can be expressed as
(A)3q,3q+1,3q+2
(B)3q
(C)none of the above
(D)3q+1

Answer 1

Given:

b = 3

To find:

If b = 3, then any integer can be expressed as

Solution:

From given, we have,

b = 3

Given is a constant and is equated to 3.

If considering b as a variable, and as it is equated to 3, then it implies that, b is a multiple of 3.

Therefore, from given options, only the second option describes b as a multiple of 3.

So, we can take q = 1, 2, 3, 4, ..........

b = 3q

when q = 1, b = 3 × 1 = 3

when q = 2, b = 3 × 2 = 6

when q = 3, b = 3 × 3 = 9 and so on.

Therefore, option (B) 3q is correct.

Answer 2

any integer can be expressed as 3q, 3q+1, 3q+2  

Step-by-step explanation:

using  Euclid division lemma

a = bq  +  r

where r  <  b

Given  b = 3

=> a = 3q  + r

r < 3

Hence r can be 0 , 1 , 2

Hence  possible values of a

a  = 3q  + 0  = 3q

a = 3q + 1

a = 3q  + 2

Hence  any integer can be expressed as

3q, 3q+1, 3q+2  

option A  is correct

Similarly if b = 2 then any integer can be expressed as

2q  , 2q + 1

Learn more:

17=6×2+5 is compared with Euclid division lemma a=bq+r then ...

https://brainly.in/question/9899330

using euclid's division Lemma Prove the difference of squares of two ...

https://brainly.in/question/16817346

Using Euclid's Division Lemma, find HCF of 54 and 90.​ - Brainly.in

https://brainly.in/question/15925833