a) (x')' = x [Using Involution Law]
b)
x + (x . y) = x(1 + y) [Using Distributive Law]
= x [Using Identity Laws]
c)
(x + y)' = x' . y' [Using DeMorgan's Law]
(x . y)' = (x' + y') [Using DeMorgan's Law]
prove properties of Boolean algebr just A B and C please! 4. Prove the following properties...
12. Prove the following properties of Boolean algebras. Give a reason for each step. a. (x + y x) b. x.(z+y) + (x' + y)' = x
2.7 Exercises 43 4. Prove each of the following identities by using the algebraic rules (no truth tables). Several steps may be combined, but make sure that each step is clear (a) a'b b'c + a'c (b) а'd + ac (c) xz' + x'y' + x'z + y'z = y' + x'z + xz' (d) ad' a'b' + c'd + a'c' + b'd = ad' + (bc' (e) xy' z(x' + y + w) (f) a'z' yz + xy' =...
Simplify the following boolean expressions. Step by step please I would like to really understand it. F(x, y, z) = xy + x’y’z’ + x’yz’ F(x, y, z) = x’yz + xy’z + xy’z + x’yz’ F(x, y, z) = xy’z’ + xz + x’y’z F(w, x, y, z) =x’z + w’xy’ + w(x’y + xy’) F(w, x, y, z) =w’x’y’x’ + wy’z’ + x’yz’ + w’xyz + xy’z
number a and b
70 Score: B. Bader collin Alhusni_ DATE Вт output E LUBODA RAO+O D ot x 1= X X-D=0 1. X+0=X XXX XX'=0 2. x + 1= 1 Idempotent laws: 3. X+X=X Involution law: 4. (X'=X Laws of complementarity: 5. X+X' = 1 Commutative laws: 6. X + Y=Y+X Associative laws: 7. (X+Y) +2=X+ (Y+Z) =X+Y+Z XY YX (XY)Z = X(YZ) = XYZ Distributive laws: 8. XIY + Z) = XY + XZ De Morgan's laws 9....
Prove the following results hold in all Boolean Algebras: (a) For all x: (x A1') V (x' 11) = x' (b) For all x,y: (x A y) V x = x (C) For all x,y: (x V y) A (x' Ay') = 0 (d) For all x,y,z: ((x V y) (y Vz)) A(Z V x) = ((x Ay) (y Az)) V (2 Ax)
7. (a) Find an example of a Boolean algebra with elements x, y, and z for which xty-x + z but yz. (b) Prove that in any Boolean algebra, if xy- z and+ yxz, then y -z
7. (a) Find an example of a Boolean algebra with elements x, y, and z for which xty-x + z but yz. (b) Prove that in any Boolean algebra, if xy- z and+ yxz, then y -z
Simplify the following Boolean expressions to the minimum number of terms using the properties of Boolean algebra (show your work and write the property you are applying). State if they cannot be simplified A. X’Y + XY B. (X + Y)(X + Y’) C. (A’ + B’) (A + B)’ D. ABC + A’B + A’BC’ E. XY + X(WZ + WZ’)
(06) Proof the following absorption theorem using the fundamental of Boolean algebra X+ XY= X (07) Use De Morgan's Theorem, to find the complement of the following function F(X, Y, Z) = XYZ + xyz (08) Obtain the truth table of the following function, then express it in sum-of-minterms and product-of-maxterms form F= XY+XZ (Q9) For the following abbreviated forms, find the corresponding canonical representations, (a) F(A, B, C) = (0,2,4,6) (b) F(X, Y, Z) = II (1,3,5,7)
c & e only please
2.1 + Demonstrate the validity of the following identities by means of truth tables: (a) De Morgan's theorem for three variables: (x + y + z)' = x'y'z' and (xyz)' = x y + z' (b) The distributive law: x + yz = (x + y)(x + z) (c) The distributive law: x(y + z) = xy + xz (e) Associative law: x(yz) = (xy)z
solve parts b,d and f
2. Compute the integral of f over S where (a) f(ayz)xy+z.S is the region in the first octant with xy+ (b) f(xy.z)xxyz, S is the region defined in 2(a) (c) f(x,y.z) x + y2-xz, s is the region bounded by the x'y plane, the plane z (d) f(x,y,z) 2, and the cylinderx2 y z, s is the region in the first octant bounded by r2 + y2 + 2 4 (e) f(xy,z-2, s is the...