Question #0970c

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Answer 1 · 2017-06-07T21:11:57

See 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: