Homework Answers
a)
(x+y.x)'
=x'.(y.x)' (demorgan's law)
=x'(y'+x') (demorgan's law)
=x'.y'+x'.x'(distributive law A.(B+C)=A.B+A.C)
=x'.y'+x' (Idempotent law A.A=A)
=x'+x'.y' (Commutative law)
=x' (absorption law A+AB=A where A=x', B=y')
b)
x.(z+y)+(x'+y)'
=x.z+x.y+(x'+y)' (distributive law)
=x.z+x.y+(x')'.(y') (demorgan's law)
=x.z+x.y+x.y' (double negation law (A')'=A)
=x.z+x.(y+y') (distributive law)
=x.z+x.1 (complement law A+A'=1)
=x.z+x
=x+xz
=x (absorption law)
c)
(x.y)'+x'.z+y'.z
=x'+y'+x'z+y'.z (demorgans law)
=x'+y'+z.(x'+y') (distributive law)
=x'+y'+(x'+y').z (commutative law)
=x'+y' (absorption law A+AB=A where A=x'+y' B=z)
Add Answer to:
12. Prove the following properties of Boolean algebras. Give a reason for each step. a. (x...
prove properties of Boolean algebr just A B and C please! 4. Prove the following properties...
prove properties of Boolean algebr
just A B and C please!
4. Prove the following properties of Boolean algebras. Give a reason for each step. * (b) x + (x-y) = x x . (x + y) x (absorption properties) (c) (x y -x'x y)' -xy(DeMorgan's Laws) x +(y (xz))(x + y) (x (modular properties) (e) (x+y)·(x, + y) = y y+ y-y y)+x)-x+y (x-y) .(y+x') = x . y g x+y'-x+ y +x y)' (h) ((x . y) ....
Prove with Boolean algebra that (x - y) + (x'-y)-y. Give a reason for each step...
Prove with Boolean algebra that (x - y) + (x'-y)-y. Give a reason for each step in your proof.
Prove the following results hold in all Boolean Algebras: (a) For all x: (x A1') V...
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)
Find the complement of Y(a,b)=ab’+a’b, and prove that Y+Y'=1. Give a reason for each step.
Find the complement of Y(a,b)=ab’+a’b, and prove that Y+Y'=1. Give a reason for each step.
Let ? be a Boolean algebra and ?,? two elements of ?. Use properties of Boolean...
Let ? be a Boolean algebra and ?,? two elements of ?. Use properties of Boolean algebras to find the solution of the equation (i.e., solve for ?x) a⋅x+b¯=0 in term of ?a and ?b according to conditions in each item. a) What is the solution set of the equation above if ?=1a=1 and ?=1b=1? Justify your answer. b) What is the solution set of the equation above if ?=1a=1 and ?=0b=0? Justify your answer.
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...
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
[8] Using properties of Boolean algebra, simplify the following Boolean expressions so they could be built...
[8] Using properties of Boolean algebra, simplify the following Boolean expressions so they could be built with the minimum number of gates. a. X= A + BC + AB + ABC + B b. Y = AB + B(AC + BC + ABC' + A) C. W = ABC' + AB'C' + B'CD + A'C + BC d. Z = (A + B')' + (ABC')' +A(B + A'C)'
Use Boolean algebra to prove that wz, + wX + y'z + x'y (w' + x'...
Use Boolean algebra to prove that wz, + wX + y'z + x'y (w' + x' + y' + z')(w + x + y + z)
Simplify the following boolean expressions. Step by step please I would like to really understand it....
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
Simplify the following Boolean expressions to the minimum number of terms using the properties of Boolean algebra (show...
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’)
prove properties of Boolean algebr
just A B and C please!
4. Prove the following properties of Boolean algebras. Give a reason for each step. * (b) x + (x-y) = x x . (x + y) x (absorption properties) (c) (x y -x'x y)' -xy(DeMorgan's Laws) x +(y (xz))(x + y) (x (modular properties) (e) (x+y)·(x, + y) = y y+ y-y y)+x)-x+y (x-y) .(y+x') = x . y g x+y'-x+ y +x y)' (h) ((x . y) ....
Prove with Boolean algebra that (x - y) + (x'-y)-y. Give a reason for each step in your proof.
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
[8] Using properties of Boolean algebra, simplify the following Boolean expressions so they could be built with the minimum number of gates. a. X= A + BC + AB + ABC + B b. Y = AB + B(AC + BC + ABC' + A) C. W = ABC' + AB'C' + B'CD + A'C + BC d. Z = (A + B')' + (ABC')' +A(B + A'C)'
Use Boolean algebra to prove that wz, + wX + y'z + x'y (w' + x' + y' + z')(w + x + y + z)
Most questions answered within 3 hours.
-
1. When a nearsighted person looks at an object that is in the
distance with their...
asked 20 minutes ago -
QUESTION 8
Both of these statements will store the same value in the
variable $number
$number...
asked 44 minutes ago -
The price of 1 lb of potatoes is $1.75. If all the potatoes sold
today at...
asked 1 hour ago -
Garcia Company issues 20.00%, 15-year bonds with a par value of
$470,000 and semiannual interest payments....
asked 1 hour ago -
In C++ Programming, Try using loops only.
This lab demonstrates the use of the While Loop...
asked 2 hours ago -
Effect of DCMU and sodium azide on Chlamydomonas? We did an
experiment where we had Chlamydomonas...
asked 3 hours ago -
1a) According to the ideal gas law, _______________.
a. a gas has infinite volume at absolute...
asked 4 hours ago -
Oakdale Fashions, Inc. had $245,000 in 2018 taxable income.
Using the tax schedule in Table 2.3...
asked 5 hours ago -
The marketing class at CSUS had an average score of 150. An
educational analyst determined that...
asked 6 hours ago -
Justin Case has purchased a $250 000 home by putting 20 % down
and taking out...
asked 6 hours ago -
1. In a labor market, marginal cost for a firm is
____________.
a. recruiting cost
b....
asked 7 hours ago -
On January 1, 2019, ABC Company issued $60,000,000 of 20-year,
10.5% bonds when the market rate...
asked 7 hours ago