1. Prove that “(∀x)Fx • (∀x)Gx” is equivalent to “(∀x)(Fx • Gx)”.
Construct expansions in a two-individual universe of discourse for the following sentences: Predicate Logic Symbolization 1. (x)(Fx ⋅ Gx) 3. (x)[Fx (Gx ∨ Hx)] 5. (x) (Fx Gx) 7. (x)(Fx Gx) 9. (x)[Fx (Gx Hx)] 11. (∃x)[(Fx ⋅ Gx) ∨ (Hx ⋅ Kx)] 13. (∃x) [(Fx Gx) ∨ (Fx Hx)]
3 3) (Ex)(Gx Fx), (Ex) (Gx Hx) ~(ax)Fx, 4) (x)(FxGx) (3x)~Gx (Ix 3) (Ex)(Gx Fx), (Ex) (Gx Hx) ~(ax)Fx, 4) (x)(FxGx) (3x)~Gx (Ix
3 (2) (x)(Ax Bx), (Ex)(Cx Bx), (x)(CXAX) (Ex) (Gx Hx) (3) (Ex)(Gx Fx), (ax)Fx, (Ex) Gx 3x) Fx (4) (x)(Fx Gx) (2) (x)(Ax Bx), (Ex)(Cx Bx), (x)(CXAX) (Ex) (Gx Hx) (3) (Ex)(Gx Fx), (ax)Fx, (Ex) Gx 3x) Fx (4) (x)(Fx Gx)
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)
14. If f(a) and g(x) are polynomials over the field F, and h(x)-f(x) t gx), prove that h(c)-f(c) + g(c) for all c in F. 15. If f(x) and g(x) are polynomials over the field F, and p(x)fx)g(x), prove that p(c) -f(c)g(c) for all c in F
If fx=2x2-3 and gx=x+64 , find the following: a) fg3 b) gf9
Need help solving this symbolic logic derivation using Logic2010. ∀x(Fx∧Gx) ∴ ∀xGx
Prove by deduction ∀x(F x -> Gx), ∃xF x ∴ ∃xGx Using rule in proofs.openlogicproject.org
Prove that fx=5ln(x-7) is not uniformly continuous on (0,∞) .