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Prove the following results hold in all Boolean Algebras: (a) For all x: (x A1') V...
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
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) ....
Given z =f(x, y) and w = g(x, y) such that a/ax = aw/ay and az/ay-みv/ar. If θι and θ2 are two mutually perpendicular directions, show that at any point FOx, y), as/as, = aw/as, and as/as, =-aw/as, . 21. Given z =f(x, y) and w = g(x, y) such that a/ax = aw/ay and az/ay-みv/ar. If θι and θ2 are two mutually perpendicular directions, show that at any point FOx, y), as/as, = aw/as, and as/as, =-aw/as, . 21.
3. In the following, consider z as a function of x and y, i.e., z = z(x, y) and use az az implicit differentiation to find the partial derivatives and ax ay (a) x2 + y2 + z2 = 3xyz (b) yz = ln(x + 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 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
(a) Is this boolean equation valid or invalid for all possible values of x,y and z? x XOR (y OR z) = (x XOR y) OR (x XOR z) (b) Prove your answer, by using a truth table
2. The defl ection a uniform beam with flexual rigidity EI and applied. be load f (x) = cos (x) satisfies the equation 2 y(0) =v'(0) = 0 11' (2)イ(2) =0 Ely(4) (x) = f (x) (a) Evaluate the deflection y (). '/ sin (a 2) dx =--cos (az)+C Hint:"/ cos (ax) dx=-sin (ax) + C, 2. The defl ection a uniform beam with flexual rigidity EI and applied. be load f (x) = cos (x) satisfies the equation 2...
(a) Implement the following Boolean functions using decoders. i) F1 = x'y z' + x Z ii) F2 = x y' z' + x' y (b) Implement the following Boolean function using multiplexers. i) F1 (a, b, c, d) = Σ(1, 3, 4, 11, 12, 13, 14, 15) ii) F2 (a, b, c, d)= Σ(1, 2, 5, 7, 8, 10, 11, 13, 15)
1. Read Only Memory Design a ROM that implements the following four Boolean functions: A(x,y,z)-2m(2, 3, 4, 5) B(x,y,z)-2m(0, 1, 2, 6) C(x,y,z) -2m(0, 3, 4, 5, 7) D(x,y,z) -2m(3, 5, 6) Make sure you are using an appropriately sized decoder, all lines are clear, and all "connections" are clearly marked. 1. Read Only Memory Design a ROM that implements the following four Boolean functions: A(x,y,z)-2m(2, 3, 4, 5) B(x,y,z)-2m(0, 1, 2, 6) C(x,y,z) -2m(0, 3, 4, 5, 7) D(x,y,z)...
This is all one question please answer asap Line Integral & Path Independency Problem 1 Prove that the vector field F = (2x – 3yz?) { +(2 – 3xz) j-6xyzk is the gradient of a scalar function f(x,y,z). Hint: find the curl of F, is it a zero vector? Integrate and find f(x,y,z), called a potential, like from potential energy? Show all your work. Then, use f(x,y,z) to compute the line integral, or work of the force F: Work of...