9. Natural Deduction for Predicate Logic. Construct natural deduction proofs for each of the following sequents. 9.1 Vx(Hx-Gx), 3x(Gx ^ Fx) End 3x(Fx ^-Hx) 9.2 3x3yFxy, VxVy(Fxy + (Gx^-Gy)) End (ExxGx - 3x-Gx) 9.3 3xVyFxy END Vy3xFxy 9.4 3x(Fx a Vy(Ty Gy)), Vx(Fx (Ey(Ay A Gy) Bxx)), 32(Az A Tz) END 3xBxx 9.5 VxVy(Fx +32(Tz v Gy)), Vx(Gx Hx) End (Ex-Hx^-32Tz) Vx-Fx) 9. Natural Deduction for Predicate Logic. Construct natural deduction proofs for each of the following sequents. 9.1 Vx(Hx-Gx), 3x(Gx ^ Fx) End 3x(Fx ^-Hx) 9.2 3x3yFxy, VxVy(Fxy + (Gx^-Gy)) End (ExxGx - 3x-Gx) 9.3 3xVyFxy END Vy3xFxy 9.4 3x(Fx a Vy(Ty Gy)), Vx(Fx (Ey(Ay A Gy) Bxx)), 32(Az A Tz) END 3xBxx 9.5 VxVy(Fx +32(Tz v Gy)), Vx(Gx Hx) End (Ex-Hx^-32Tz) Vx-Fx)