Q2 of 34 Page 174

Taking different numbers, positive negative and zero, as x, y, z and compute x + (y + z) and (x + y) + z. Check whether the equation, x + (y + z) = (x + y) + z holds for all these numbers.

Let’s take x = 0,1,-1 y = 1,0,-1 and z = -1,1,0 respectively.

CASE 1: When x = 0, y = 1 and z = -1


Then, x + (y + z),


= 0 + (1-1)


= 0


CASE 2: When x = 1, y = 0 and z = 1


Then, x + (y + z)


= 1 + (0 + 1)


= 2


CASE 3: When x = -1, y = -1 and z = 0,


Then, x + (y + z)


= -1 + (-1 + 0)


= -2


Calculating (x + y) + z


CASE 1: When x = 0, y = 1 and z = -1


= (0 + 1) + (-1)


= 0


CASE 2:When x = 1, y = 0 and z = 1


= (1 + 0) + 1


= 2


CASE 3:When x = -1, y = -1 and z = 0


= (-1-1) + 0


= -2


Since, in every case x + (y + z) = (x + y) + z so,this holds for all these numbers.


More from this chapter

All 34 →
1

Check whether the equations are identities. Write the patterns got form each,on taking x = 1, 2, 3, 4, 5 and x = –1, –2, –3, –4, –5.

–x + (x + 1) + (x + 2) – (x + 3) = 0

 1

Check whether the equations are identities. Write the patterns got form each,on taking x = 1, 2, 3, 4, 5 and x = –1, –2, –3, –4, –5.

–x – (x + 1) + (x + 2) + (x + 3) = 4

 1

Take various positive and negative numbers as x, y, z and compute (x + y)z and xz + yz. Check whether the equation (x + y)z = xz + yz holds for all these.

 2

In each of the following equations, take x as the given numbers and compute the numbers y.

y = x2, x = –5, x = 5