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
Answers
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.
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
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