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
Linear Algebra Proof Pon 2. Prove: Additive Inverse of v
Linear Algebra Please show details. Thank you. 36. Proof Prove that if A and B are similar matrices and A is nonsingular, then B is also nonsingular and A-1 and B-1 are similar matrices.
Define f: R2R by 224V2 y) (0,0) 0 if (x, y)-(0,0) if (z, f(z, y) (a) Prove that Dif(z, y) and D2f (x, y) exist for each (x, y) E R2. (b) Prove that f is not continuous at (0,0).
Prove with Boolean algebra that (x - y) + (x'-y)-y. Give a reason for each step in your proof.
(3) If z = a + ib E C and |2| := Va² + b², prove that |zw| = |z||w]. Proof. Proof here. goes (4) Let y : C× → R* be defined by 9(z) = |z|. Use Problem (3) to prove that y is a homomorphism. Proof. Proof goes here.
Q2: 1. Proof this Boolean expression. Use Boolean Algebra (X+Y). (Z+W).(X'+Y+W) = Y.Z+X.W+Y.W 2. For this BF F(X,,Z)=((XYZ)(X +Z))(X+Y) • Design the digital circuit Derive the Boolean Function of X, Y, Z. Simplify the Function Derive the truth table before and after simplification. Derive the BF F(X,Y,Z) as Maxterms (POS) and miterms (SOP). Implement the F(X,Y,Z) after simplification using NAND gates only. Implement the F(X,Y,Z) after simplification using OR NOR gates only.
in 3rd question it ask "z=z(x,y), if Z=x*f(y/x) proof x*Zx+y*Zy=z equation " and in 4th question it ask draw integration area, calculate the integration and change integration line. (x,y)–(0,0) x2 + y 3) = = z (x,y) olmak üzere z = xf (9) ise 2 tyzy = oldi 4 2 Dj sin (2²) dady 0 y/2
(a) Prove that l-x」=-[al and「-2] =- (b) Give a proof by cases that 142] = 1x1+ 1xH + 1x-si + 1x+1 . 3
Advanced Linear Algebra (bonus problem) 1. (This question guides you through a different proof of part of the Decomposition Theorem. So you are not allowed to use the Decomposition Theorem when answering this question.) Let F be a field and V an n-dimensional F-vector space for n > I. Let θ E End(V) be a linear transformation and α E F an eigenvalue of. Recall that the generalised α-eigenspace of θ is a) Suppose that 0 υ Ε να and...