Question #0970c

1 Answer
Jun 7, 2017

Answer:

See explanation...

Explanation:

From:

#EE x not P(x)#

we have some #x_1# such that #not P(x_1)#

Then:

#AAx(P(x)vvQ(x)) |-- P(x_1)vvQ(x_1)#

Then:

#(P(x_1)vvQ(x_1))^^not P(x_1) |-- Q(x_1)#

We have

#AAx(not Q(x)vvS(x)) |-- not Q(x_1) vv S(x_1)#

Then:

#(not Q(x_1) vv S(x_1)) ^^ Q(x_1) |-- S(x_1)#

We have:

#AAx(R(x)->not S(x)) |- R(x_1)->not S(x_1)#

Then:

#(R(x_1)->not S(x_1)) ^^ S(x_1)->not R(x_1)#

Finally:

#not R(x_1) |-- EEx not R(x)#

#color(white)()#
Rules used

The rules we have used are:

  • #EExP(x) |-- P(x_1)" "# for some #x_1#

  • #AAxP(x) |-- P(x_1)" "# for any #x_1#

  • #(PvvQ)^^not P |-- Q#

  • #(not P vv Q) ^^ P |-- Q#

  • #(P->not Q) ^^ Q |-- not P#