edited by
4,118 views
8 votes
8 votes

Which of the following is not valid Boolean algebra rule?

  1. $\text{X.X = X}$
  2. $\text{(X+Y).X = X}$
  3. $\overline{X}+\text{XY = Y}$
  4. $\text{(X+Y).(X+Z) = X + YZ}$
edited by

4 Answers

Best answer
10 votes
10 votes
Answer is C

x' + xy = (x' + x)(x' + y) = x' + y
selected by
4 votes
4 votes
ans is C x'+xy =(x'+x)(x'+y)=1.(x'+y)=x'+y which is not equal to y

a)is true as X.X=X    b)(X+Y).X=XX+XY=X+XY=X(1+Y)=X IS ALSO TRUE

D)is true as xx+xz+yx+yz=x+xz+yx+yz=x(1+z+y)+yz=x+yz
edited by
2 votes
2 votes
$X.X = X $OPTION(A) TRUE

$(X+Y)X = X+XY=X(1+Y)=X $OPTION (B) TRUE

$(X’+XY) = (X’+X)(X’+Y) = X’+Y ≠ Y$ OPTION (C) FALSE

$(X+Y)(X+Z) = XX+XZ+XY+YZ=X+XZ+XY+YZ=X(1+Z+Y) + YZ = X+YZ$ OPTION (D) TRUE

so only false rule is c

answer (c)
1 votes
1 votes
A.X.X=X is valid

B.(X+Y)X=X is valid using truth table.

C.X'+XY=Y is not valid using truth table

D.(X+Y)(X+Z)=X+YZ is valid by absorption rule
Answer:

Related questions

9 votes
9 votes
5 answers
1
go_editor asked Jul 1, 2016
5,262 views
Consider the logic circuit given below.The inverter, AND and OR gates have delays of $6, 10$ and $11$ nanoseconds respectively. Assuming that wire delays are negligible, ...
7 votes
7 votes
3 answers
2
go_editor asked Jul 1, 2016
3,754 views
The output of a tristate buffer when the enable input in $0$ isAlways $0$Always $1$Retains the last value when enable input was highDisconnected state
8 votes
8 votes
4 answers
4
jenny101 asked Jun 14, 2016
6,349 views
How many different $\text{BCD}$ numbers can be stored in $12$ switches ? (Assume two position or on-off switches).$2^{12}$$2^{12}-1$$10^{12}$$10^3$