Prove Valid: 1. (z)(Pz --> Qz) 2. (Ex) [(Oy • Py) --> (Qy • Ry)] 3. (x) (-Px v Ox) 4. (x) (Ox --> -Rx) ... :. (Ey) (-Py v -Oy) 1. (x) [(Fx v Hx) --> (Gx • Ax)] 2. -(x) (Ax • Gx) ..... :....

Question

Question

Prove Valid:

1. (z)(Pz --> Qz)
2. (Ex) [(Oy • Py) --> (Qy • Ry)]
3. (x) (-Px v Ox)
4. (x) (Ox --> -Rx)

... :. (Ey) (-Py v -Oy)

1. (x) [(Fx v Hx) --> (Gx • Ax)]
2. -(x) (Ax • Gx)

..... :. (Ex) (-Hx v Ax)

1. (x) (Px --> [(Qx • Rx) v Sx)]
2. (y) [(Qy • Ry) --> - Py]
3. (x) (Tx --> -Sx)

.... :. (y) (Py --> -Ty)

Answer 1

Answer #1

Answer 2

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function DH_MatrixTest2(LN); syms L6 L4 L4=4; L6=0.5; L5=3.5; %This inputs the form of [Nx,Ox,Ax,Px;Ny,Oy,Ay,Py;Nz,Oz,Az,Pz;0,0,0,1] into %the...

function DH_MatrixTest2(LN); syms L6 L4 L4=4; L6=0.5; L5=3.5; %This inputs the form of [Nx,Ox,Ax,Px;Ny,Oy,Ay,Py;Nz,Oz,Az,Pz;0,0,0,1] into %the function-> DH_MatrixTest(([Nx,Ox,Ax,Px;Ny,Oy,Ay,Py;Nz,Oz,Az])) Nx=(LN(1,1)); Ny(LN(1,2)); Nz(LN(1,3)); Ox(LN(1,4)); Oy(LN(1,5)); Oz=(LN(1,6)); Ax=(LN(1,7)); Ay=(LN(1,8)); Az=(LN(1,9)); Px=(LN(1,10)); Py=(LN(1,11)); Pz=(LN(1,12)); T_matrix=[Nx,Ox,Ax,Px; Ny,Oy,Ay,Py; Nz,Oz,Az,Pz; 0,0,0,1] %display the original T %matrix theta1=(atan2d(Py,Px)) % theta1=theta1 + pi theta234=(atan2d(Az,Ax*cosd(theta1)+Ay*sind(theta1))) %display theta234 %theta234=theta234 + pi C3=((Px*cosd(theta1)+Py*sind(theta1)-cosd(theta234)*L6)^2 +(Pz-sind(theta234))^2 -L4^2 - L5^2)/(2*L4*L5) %display C3 S3=(1-C3^2)^.5 %display S3 theta3=atan2d(S3,C3) %display theta3 %display theta2 below: theta2=atan2d(((C3*L5+L4)*(Pz-sind(theta234)*L6) - S3*L5*(Px*cosd(theta1)+Py*sind(theta1) - cosd(theta234)*L6)), ((C3*L5+L4)*(Px*cosd(theta1)+Py*sind(theta1) - cosd(theta234)*L6) +...