Provide the missing reasons for the steps verifying the following argument: Steps Reasons (1) x [p(x) ¨

Provide the missing reasons for the steps verifying the following argument:

Steps Reasons
(1) ˆ€x [p(x) ˆ¨ q(x)] Premise
(2) ˆƒx ¬p(x) Premise
(3) ¬ p(a) Step (2) and the definition of the truth for ˆƒx ¬ p(x).
[Here a is an element (replacement) from the universe
for which ¬p(x) is true.] The reason for this step is also
referred to as the Rule of Existential Specification.
(4) p(a) ˆ¨ q(a)
(5) q(a)
(6) ˆ€x [¬q(x) ˆ¨ r(x)]
(7) ¬q(a) ˆ¨ r(a)
(8) q(a) †’ r(a)
(9) r(a)
(10) ˆ€x [s(x) †’ ¬ r (x)]
(11) s(a) †’ ¬ r(a)
(12) r(a) †’ ¬s(a)
(13) ¬s(a)
(14) ˆ´ ˆƒx ¬s(x) Step (13) and the definition of the truth for ˆƒx ¬s(x).
The reason for this step is also referred to as the Rule
of Existential Generalization.

Transcribed Image Text:

Vr [P(x) ν q(x)] Vr [s(x) →-r (x)) ax -s(x)