tell me the answer please
Answers
(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∗(
2
−1
∗
4
1
)
= 1 * (\frac{-1}{8} )1∗(
8
−1
)
= \frac{-1}{8}
8
−1
( x * y ) * z [R.H.S]
= (1 * \frac{-1}{2} ) * \frac{1}{4}(1∗
2
−1
)∗
4
1
= \frac{-1}{2} * \frac{1}{4}
2
−1
∗
4
1
= \frac{-1}{8}
8
−1
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} )
3
2
∗(
7
−3
∗
2
1
)
= \frac{2}{3} * \frac{-3}{14}
3
2
∗
14
−3
= \frac{-6}{42}
42
−6
( x * y ) * z [R.H.S]
= (\frac{2}{3} * \frac{-3}{7} ) * \frac{1}{2}(
3
2
∗
7
−3
)∗
2
1
= \frac{-6}{21} * \frac{1}{2}
21
−6
∗
2
1
= \frac{-6}{42}
42
−6
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} )
7
−2
∗(
6
−5
∗
4
1
)
= \frac{-2}{7} * \frac{-5}{24}
7
−2
∗
24
−5
= \frac{10}{168}
168
10
( x * y ) * z [R.H.S]
= (\frac{-2}{7} * \frac{-5}{6} ) * \frac{1}{4}(
7
−2
∗
6
−5
)∗
4
1
= \frac{10}{42} * \frac{1}{4}
42
10
∗
4
1
= \frac{10}{168}
168
10
Hence verified.
Hope this helps you dear!!!