Question

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Answer 1

a) x*(y*z) = (x*y)*z

1*($\frac{-1}{2} * \frac{1}{4}$) = $(1 * \frac{-1}{2} ) * \frac{1}{4}$

$1 * \frac{-1}{8} = \frac{-1}{2} * \frac{1}{4}$

$\frac{-1}{8} = \frac{-1}{8}$

As LHS = RHS, the property is correct .

Hence, verified.

b) x*(y*z) = (x*y)*z

$\frac{2}{3}* (\frac{-3}{7} * \frac{1}{2} ) = (\frac{2}{3}* \frac{-3}{7}) * \frac{1}{2}$

$\frac{2}{3} * \frac{-3}{14} = \frac{-6}{21} * \frac{1}{2} \\\\\frac{-6}{42} = \frac{-6}{42}$

LHS = RHS

Hence, verified.

Answer 2

Step-by-step explanation:

A.

X×(Y×Z) =(X×Y) ×Z

PUT THE VALUE OF X, Y and Z

1(-1/2×1/4)=(1×-1/2)×1/4

1(-1/8)=(-1/2)×1/4

-1/8=-1/8

L.h.s=R.h.s(proved)

B.

X×(Y×Z) =(X×Y) ×Z

PUT THE VALUE OF X, Y, AND Z

2/3(-3/7×1/2)=(2/3×-3/7)1/2

2/3(-3/14)=(-2/7)1/2

2/3×-3/14=-2/7×1/2

-1/7=-1/7

L.h.s=R.h.s (proved)