Question

Rational numbers do not satisfy associative property with respect to subtraction.Very with example

Answer 1

Associative property with respect to subtraction:

    If a, b, c are three rational numbers then if it satisfies associative property, then

   →   (a -b)-c≠a-(b-c)

We will check this property using, a=5/2, b= -9/2, c=11/2

Left hand side: (a-b)-c= [5/2 - (-9/2)] -11/2=5/2+9/2-11/2=14/2 -11/2=3/2

Right hand side: a -(b-c)=5/2 -[ -9/2 - 11/2]= 5/2 - [-20/2]=5/2+ 10=25/2

As, you can see ,L.H.S ≠ R.H.S i.e ⇒3/2≠ 25/2

So,  (a -b)-c≠a-(b-c) which shows that Rational numbers do not satisfy associative property with respect to subtraction.