User:Omphaloscope/Logic homework

Logic

p. 115

$$B2.\ (x) \lnot\ Gx$$

$$B5.\ (\exists x)(Gx \land Px)$$

$$B10.\ (\exists x)Gx \supset (\exists x)(Gy \land \lnot Py)$$

$$B12.\ (x)(Gx \equiv \lnot Px)$$

p. 120

$$C4.\ (x)(Tx \supset \lnot Mx)$$

$$C6.\ (x)(Mx \supset \lnot Tx)$$

$$C9.\ (\exists x)Tx \supset (\exists x)Py$$

$$C12.\ (\exists x)(Px \land \lnot Mx \land \lnot Tx)$$

p. 138

$$1.\ (\exists x)(\exists x)Ixy$$

$$2.\ (x)(y)Ixy$$

$$3.\ (\exists x)(y)Ixy$$

$$4.\ (y)(\exists x)Ixy$$

$$5.\ \lnot(\exists x)(y)Ixy$$

$$6.\ (x)(y) \lnot Ixy$$

$$7.\ (x)(\exists y) Ixy$$

$$8.\ (\exists x)(\exists x) \lnot Ixy$$

$$12.\ (x)(\exists y)(Ixx \supset Ixy)$$

$$15.\ (x)(y)(Ixy \supset Ixx)$$