Find the variable assignment that solves the following horn formulas:
1. (w∧y∧z) ⇒ x,(x∧z) ⇒ w, x ⇒ y,⇒ x,(x∧y) ⇒ w,(w¯ ∨x¯,∨y¯),(z¯)
2. (x∧z) ⇒ y,z ⇒ w,(y∧z) ⇒ x,⇒ z,(z¯∨x¯),(w¯ ∨y¯∨z¯)
please provide fully explanation.
Find the variable assignment that solves the following horn formulas: 1. (w∧y∧z) ⇒ x,(x∧z) ⇒ w,...
a. Find a satisfying assignment for the following boolean
formula:
(x
y
z')
( x
y'
z)
(w'
x
y')
(w'
x'
z)
b. What is the number of satistifying assignments for the
boolean formula listed above.
1. Find 8 different 2-level minimized circuits to realize each of the following functions. 1. F(W,X,Y,Z) = {m (2,4,6,7,12,14,15) 2. G(W,X,Y,Z) = (x + Y' + Z) (X' + Y + Z) W • Using algebraic techniques • Using network conversion
Find 8 different 2-level minimized circuits to realize each of the following functions. 1. F(W,X,Y,Z) = ∑m (2,4,6,7,12,14,15) 2. G(W,X,Y,Z) = (X + Y’ + Z) (X’ + Y + Z) W • Using algebraic techniques • Using network conversion
6.8. Verify that u(x, y)= A sin(27Tx) sin(27ty) solves Poisson's equation V2u-Ron W (0, 1) x (0,1) for some A-value, where R(x, y) sin(2x) sin(2Ty) (a) Find the correct A value (b) Compute the total source S w RdA (c) Compute the flux out through the top part of W (y 1) and verify by symmetry that it is one-quarter that of the full source S.
6.8. Verify that u(x, y)= A sin(27Tx) sin(27ty) solves Poisson's equation V2u-Ron W (0,...
for the sample space {w,x,y,z}, p(x)=0.2, p(y)=0.15, p({w,y})=0.7, p({x,z})=0.3. Find p(w), p(z), and p({w,x,z}), using the properties of probability.
Simplify the following Boolean functions using four-variable maps: F(w, x, y, z) = Σ (1, 4, 5, 6, 12, 14, 15) F(w, x, y, z) = Π (0, 1, 4, 5, 6, 7, 8, 9) AB’C + B’C’D’ + BCD + ACD’ + A’B’C+ A’BC’D (A xor B)’ (C xor D)
Is W = {(x, y, z, w) | x − y = 2z + w & w − y = 2x + 3z} a subspace? Justify your answer. If it’s a subspace, find a basis for W and compute dim W.
3) Suppose that w = f(x, y, z) = ln(x y2z3). a) (20 pts.) Find the unit vector in the direction of most rapid increase in w at the point (x,y,z) = (1,-2,-3) b) (15 pts.) Find the rate of change in w in this direction at (1,-2,-3).
F = W ⋅ X ⋅ Y ⋅ Z ⋅ (W ⋅ X ⋅ Y ⋅ Z′ + W ⋅ X′ ⋅ Y ⋅ Z + W′ ⋅ X ⋅ Y ⋅ Z + W ⋅ X ⋅ Y′ ⋅ Z) With switching algebra, what would it be simplified
5] (2) GIVEN: a> 0,0# {(x, y, z) z a"-x'-y") W is the solid region of R' that is below 2 and above the xy- plane. W has constant density,8 and the mass of W is M, m(W) M FIND: The moment of inertia, I, of W with respect to the z- axis, express 2 I in terms of M and a without 8