Sadowski wrote:gabriel wrote:Shadow wrote:gabriel wrote:sahaldar wrote:1. xy+z=x(y+z) which of the following must be true.
a) x=0 and z=0
b) x=1 and y=1
c) y=1 and z=0
d) x=1 or y=0
e) x=1 or z=0
All the given anwsers satisfies the equation. why the anwser is (d)
we have xy+z=x(y+z) .. which boils down to z=xz .. to satisfy this condition there are 2 possiblities
first x = 1 .. in which case z = 1*z ..that is z=z ...
second z= 0 .. in which case 0=x*0 .. that is 0=0 ..
so the the answer should be e
It should be D
The equation boils down to z=xz
Cancelling z on both sides we get 1=x
so the value of x=1
so we can eliminate choice A and C
Again having a look into the equation,
xy+z=xy+xz
Put y=0, we get 1=x
So the choice should be D.
our aim over here is not to prove that x= 1 .. our aim is to find the condition under which the equation xy+z=x(y+z) is true ..
...by putting x= 1 we get y+z=y+z .. that is the equation is true if x = 1
... by putting z=0 we get xy = xy that is we again prove that the equation is true .. if z= 0
remeber we are not trying to find the value of any variable over here .. but are trying to find the conditions under which a seemingly unequal equation is equal ..
I must be missing something. Your logic makes sense, but it doesn't prove why other answers are incorrect. For instance, choosing option C (y=1, z=0) we get x=x. This proves that the equation is true just as well as choice D proves it.
... the question over here is not what can be true but it is what
must be true ...
... take a close look at the given equation .. xy+z=x(y+z) .. that is xy + z = xy +xz ...
.. as we can see xy is eliminated from both the sides and the eqn boils down to z = xz .. that means y is out of the picture .. that is it doesnt matter what value y takes bcoz eventually the terms with y are eliminated from the eqn .. y can take a value of 10 million ..still doesnt matter ..
now look at the equation that is left that is z = xz ... suppose z = 200 ... we have 200 = x 200 ... for this to be true x must be 1 ... what if the value of x = 2 ..we have z = 2*z .. which can never be true .. so for the eqn xy+z = x(y+z) to be true x has to be 1 ...
.. the other possiblity for the eqn z = xz to be true is that both sides are equal to 0 ... for that to be true z must be 0 ..
.. these are the only 2 ways the above eqn is true .. so the answer is z=0 or x = 1 .. remember it is about what must be true not what can be true ...
