Question

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Answer 1

Answer:

Step-by-step explanation:

(a) (a) x = 1 , y = -1/2 , z = 1/4

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

=   x * ( y * z )   [L.H.S]

=  $1 * (\frac{-1}{2} *\frac{1}{4} )$

= $1 * (\frac{-1}{8} )$

=  $\frac{-1}{8}$

( x * y ) * z [R.H.S]

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

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

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

Hence verified.

(b) x = 2/3 , y = -3/7 , z = 1/2

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

=   x * ( y * z )   [L.H.S]

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

= $\frac{2}{3} * \frac{-3}{14}$

= $\frac{-6}{42}$

( x * y ) * z [R.H.S]

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

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

= $\frac{-6}{42}$

Hence verified.

(c) x = -2/7 , y = -5/6 , z = 1/4

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

=   x * ( y * z )   [L.H.S]

= $\frac{-2}{7} * (\frac{-5}{6} * \frac{1}{4} )$

= $\frac{-2}{7} * \frac{-5}{24}$

= $\frac{10}{168}$

( x * y ) * z [R.H.S]

= $(\frac{-2}{7} * \frac{-5}{6} ) * \frac{1}{4}$

= $\frac{10}{42} * \frac{1}{4}$

= $\frac{10}{168}$

Hence verified.

Hope this helps you dear!!!