Use rules of inference to show that if ∀ x ( P ( x ) ∨ Q ( x ) ) and ∀ x ( ( ¬ P ( x ) ∧ Q ( x ) ) → R ( x ) ) are true, then ∀ x ( ¬ R ( x ) → P ( x ) ) is also true, where the domains of all quantifiers are the same.
Use rules of inference to show that if ∀ x ( P ( x ) ∨ Q ( x ) ) and ∀ x ( ( ¬ P ( x ) ∧ Q ( x ) ) → R ( x ) ) are true, then ∀ x ( ¬ R ( x ) → P ( x ) ) is also true, where the domains of all quantifiers are the same.
Use rules of inference to show that if
∀
x
(
P
(
x
)
∨
Q
(
x
)
)
and
∀
x
(
(
¬
P
(
x
)
∧
Q
(
x
)
)
→
R
(
x
)
)
are true, then
∀
x
(
¬
R
(
x
)
→
P
(
x
)
)
is also true, where the domains of all quantifiers are the same.
Use rules of inference to show that if Vx(P(x) (Q(x) A S(x))) and
Vx(P(x) A R(x)) are true, then Vx(R(x) A S(x)) is true.
(Note: All the steps must be explained by reasons.)
Use rules of inference to show Vx(R(x) v P(x)) is a valid consequence of the two premises:
if Vx(P(x) V (Q(x)) and
Vx(-P(x) A Q(x) → R(x))
Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)
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MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY