Question

Please explained using the inference rules and also show all steps. In each part below, give a formal proof that the sentence given is valid or else provided an interpretation in which the sentence is false.

(a) ∀xP' (x) → ∃x[P(x) → Q'(x)].

(b) ∃x[P(x) → Q'(x)] → ∃xP' (x).

Answer #1

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Please explained using the inference rules and also show all
steps.
In each part below, give a formal proof that the sentence given
is valid or else provided an interpretation in which the sentence
is false.
(a) ∀xP' (x) → ∃x[P(x) → Q'(x)].
(b) ∃x[P(x) → Q'(x)] → ∃xP' (x).

Please explained using formal proofs in predicate logic
In each part below, give a formal proof that the sentence given
is valid or else provided an interpretation in which the sentence
is false.
(a) ∀xP' (x) → ∃x[P(x) → Q' (x)].
(b) ∃x[P(x) → Q' (x)] → QxP' (x).

In each part below, give a formal proof that the sentence given
is valid or else provided an interpretation in which the sentence
is false.
(a) [∀xA(x) ∨ ∀xB(x)] → ∀x[A(x) ∨ B(x)].
(b) [∃xA(x) ∧ ∃xB(x)] → ∃x[A(x) ∧ B(x)].

Please show all steps, thank you!
a) Verify that the functions below solve the system:
x(t) = c1e^5t + c2e^-t
y(t) = 2c1e^5t - c2e^-t
Do not solve the system
dx/dt = x + 2y
dy/dt = 4x +3y
b) Solve the system using Operator D elimination. Write the
answer both in scalar and vector form. Please show all steps!
dx/dt = x + 2y
dy/dt = 4x + 3y

Hello! I hope you are healthy and well! I am hoping that this
message finds you happy and content!
I am having trouble solving this 5-part practice problem. I
would greatly appreciate any and all help that you could lend!
Thanks in advance!
Given that A and B are true and X and Y are false, determine the
truth values of the propositions in the following problem:
∼[(B • ∼X) ⊃ ∼(Y • ∼B)] ⊃ [∼(X ⊃ A) ∨
(B...

Please show all steps to the first order equation, using
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a) solve:
y' - y = 0
b) solve:
(x-3)y' + 2y = 0

For each part below, give an example of a linear system of
three equations in three variables that has the
given property. in each case, explain how you got your answer,
possibly using sketches.
(a) has no solutions
(b) has exactly one solution which is (1, 2, 3).
(c) any point of the line given parametrically be (x, y, z) = (s
− 2, 1 + 2s, s) is a solution and nothing else is.
(d) any point of the...

please show all steps
Q.9 The number of times a batter gets to bat in a game
follows a binomial distribution N ∼ Binomial(6, 0.8). Given the
number of times N = n that the better has at bat, the number of
hits he gets conditionally follows a binomial distribution as well,
(X|N = n) ∼ Binomial(n, 0.3)
(a) Find E[X]
(b) Find Var[X]
(c) Find Cov[X, N]
(d) Find ρ[X, N]

Please show all steps, thank you.
Using the Taylor formula for f(x+h) and f(x-h) with f ''' in the
error term, find the error of the approximate formula f '' (x) =
(f(x+h)+f(x-h)-2f(x))/(h^2) in terms of f ''' (eta), for some point
eta between x-h and x+h. Then give an upper bound for the absolute
error assuming that |f ''' (t)| =< M for t between x-h and
x+h.

Consider the following (true) statement:
“All birds have wings but some birds cannot fly.”
Part 1
Write this statement symbolically as a conjunction of two
sub-statements, one of which is a conditional and the other is the
negation of a conditional.
Use three components (p, q, and r)
and explicitly state what these components correspond to in the
original statement.
Hint: Any statement in the form "some X cannot Y"
can be rewritten equivalently as “not all X can Y,”...

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