Show that F(x, y, z) = xy + xz + yz has the value 1 if and only if at least two of the variables x, y, and z have the value 1.
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- Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X BFind the values, if any, of the Boolean variable x that satisfy these equations. a) x · 1 = 0 b) x + x = 0c) x · 1 = x d) x · ??̅ = 1Suppose that a parachutist with linear drag (m=50 kg, c=12.5kg/s) jumps from an airplane flying at an altitude of a kilometer with a horizontal velocity of 220 m/s relative to the ground. a) Write a system of four differential equations for x,y,vx=dx/dt and vy=dy/dt. b) If theinitial horizontal position is defined as x=0, use Euler’s methods with t=0.4 s to compute the jumper’s position over the first 40 s. c) Develop plots of y versus t and y versus x. Use the plot to graphically estimate when and where the jumper would hit the ground if the chute failed to open.
- Find all the prime implicants for the following Boolean functions, and determine which are essential: F (w, x, y, z)=Σ(0, 1, 2, 5, 7, 8, 10, 15)solve problem D Given the Boolean function: F = xy' + z'y'z + xyz d) List the truth table or the functlon from the simplified expression and show that it is the same as the truth table in part (a).1. Simplify the following Boolean functions, using three-variable Kmaps: (a) F(x, y, z) = Σ(0, 1, 5, 7) (b) F(x, y, z) = Σ(1, 2, 3, 6, 7) (c) F(x, y, z) = Σ(2, 3, 4, 5)
- Using DeMorgan’s Law, write an expression for thecomplement of F if F(x, y, z) = xy′(x + z).Show that the function F(x,y,z) = xy + xz + yz will have a value of 1 if there are at least 2 variables x,y and z which have a value of 1. (using a table)Draw the graph of the function f(x)=⌊x/2⌋ from R to R.