Question

Which of the following are correct for P(x,y,z)= xyz + x(yz)' + x'(y + z) + (xyz)' ?

1) P(0, 0, 1) = 0

2) P(0, 1, 0) = 1

3) P(0, 0, 0) = 1

4) P(1, 1, 1) = 1

5) P(1, 0, 0) = 0

Answer 1

Question

Answer 1) (Incorrect )

As we know that  P(0, 0, 1) = 0 ----(1)

where x=0 , y=0 , z=1 and given equation is :

  P(x,y,z)= xyz + x(yz)' + x'(y + z) + (xyz)'.

Sol :-

   P(0,0,1) = 0 + 0(1) + 1(1) + 1 = 2 Hence  it is not equal to Equation ( 1 )

2) (Incorrect )

As we know that  P(0, 1, 0) = 1 ----(2)

where x=0 , y=1 , z=0   and given equation is :

  P(x,y,z)= xyz + x(yz)' + x'(y + z) + (xyz)'.

Sol :-

   P(0,1,0) = 0 + 0(1) + 1(1) + 1 = 2 Hence  it is not equal to Equation ( 2 )

3) (correct )

As we know that  P(0, 0, 0) = 1 ----(3)

where x=0 , y=0 , z=0   and given equation is :

  P(x,y,z)= xyz + x(yz)' + x'(y + z) + (xyz)'.

Sol :-   

   P(0,0,0) = 0 + 0(1) + 1(0) + 1 = 1   Hence  it is equal to Equation ( 3 )

  

4) (correct )

As we know that  P(1, 1, 1) = 1 ----(4)

where x=1 , y=1 , z=1   and given equation is :

  P(x,y,z)= xyz + x(yz)' + x'(y + z) + (xyz)'.

Sol :-

   P(1,1,1) = 1 + 1(0) + 0(2) + 0 = 1   Hence  it is equal to Equation ( 4 )

5) (Incorrect )

As we know that  P(1, 0, 0) = 0 ----(5)

where x=1 , y=0 , z=0   and given equation is :

  P(x,y,z)= xyz + x(yz)' + x'(y + z) + (xyz)'.

Sol :-

   P(1,0,0) = 0 + 1(1) + 0(0) + 1 = 2   Hence  it is not equal to Equation ( 5 )