Which relation is true for the remainder r in a = bq + r for dividend a and divisor b. 

Concept -

In the equation �=��+��=��+��=��+��=��+��=��+��=��+� a = bq+r, where ������ � � � � � a is the dividend, ������ � � � � � b is the divisor, ������ � � � � � q is the quotient, and ������ � � � � � r is the remainder:

The remainder ������ � � � � � r is the integer left over when ������ � � � � � a is divided by ������ � � � � � b. It's always non-negative and smaller than the divisor ������ � � � � � b.

Explanation -

In the equation �=��+��=��+��=��+��=��+��=��+��=��+� a = bq+r, where ������ � � � � � a is the dividend, ������ � � � � � b is the divisor, ������ � � � � � q is the quotient, and ������ � � � � � r is the remainder, the relation that holds true regarding the remainder ������ � � � � � r is:

The remainder ������ � � � � � r must be greater than or equal to zero and less than the absolute value of the divisor ������ � � � � � b.

In other words:

0≤�<∣�∣0≤�<∣�∣0≤�<∣�∣0≤�<∣�∣0≤�<∣�∣0≤�<∣�∣ 0<mo>≤<mi>�<mo><<mi mathvariant="normal">∣<mi>�<mi mathvariant="normal">∣</mi></mi></mi></mo></mi></mo> 0<mo>≤<mi>�<mo><<mi mathvariant="normal">∣<mi>�<mi mathvariant="normal">∣</mi></mi></mi></mo></mi></mo> 0<mo>≤<mi>�<mo><<mi mathvariant="normal">∣<mi>�<mi mathvariant="normal">∣</mi></mi></mi></mo></mi></mo> 0<mo>≤<mi>�<mo><<mi mathvariant="normal">∣<mi>�<mi mathvariant="normal">∣</mi></mi></mi></mo></mi></mo> 0<mo>≤<mi>�<mo><<mi mathvariant="normal">∣<mi>�<mi mathvariant="normal">∣</mi></mi></mi></mo></mi></mo> 0 ≤ r < ∣b∣   or 0 ≤ r < b

This means that the remainder ������ � � � � � r is a non-negative number and is always smaller than the absolute value of the divisor ������ � � � � � b.

Hence option (3) is true.