Question

Write down the inference or replacement rule and the line(s) it uses

(1) A -> [(AvB) -> (C•D)]

(2) [A • (AvB)] -> (C•D) ______

(1) (A • B) v (~A • B)

(2) (~A • B) v (A •B) _________

(1) (P • Q)

(2) (P • Q) -> ~ (A v B)

(3) ~ (A v B) _________

1) A• (B v C)

(2) [A• (B v C)] v [~A• ~(B v C)] ___________

(1) (A•B) ≡ (C•D)

(2) [((A•B) -> (C•D)] • [(C•D) -> (A•B)] _____________

Use the inference and replacement rules to show that these are valid arguments

(1) ∼R ⋁ P (p)

(2) ~P ⋁ R (p) / R ≡ P

(3)

(4)

(5)

(6)

(1) H -> B (p)

(2) ∼(B · A) (p) / H -> ~A

(3)

(4)

(5)

(1) A•~~B (p) / ~(~B•~C) • A

(2)

(3)

(4)

(5)

(6)

Use the 18 inference and replacement rules to show that these are valid arguments

(1) ∼R ⋁ P (p)

(2) R ⋁ ∼P (p) / R ≡ P

(3)

(4)

(5)

(6)

(7)

(1) C -> (T -> L) (p)

(2)
~L
(p)

(3)
T
(p) /~C

(4)

(5)

(6)

(7)

(8)

Answer #1

4 Inference proofs
Use laws of equivalence and inference rules to show how you can
derive the conclusions from the given premises. Be sure to cite the
rule used at each line and the line numbers of the hypotheses used
for each rule.
a) Givens:
1 a∧b
2 c → ¬a
3 c∨d
Conclusion: d
b) Givens
1 p→(q∧r)
2 ¬r
Conclusion ¬p

Derive the conclusions from the premises in the arguments below
by utilizing inference rules: [45-3] C: ~(A V C) 1: A -> B 2: C
-> D 3: (B V D) -> E 4: ~E

Part IV: All of the following arguments are VALID. Prove
the validity of each using NATURAL DEDUCTION.
1)
1. H É I
2. U v ~I
3. ~U
4. H v
S
/ S
2)
1. (I × E) É (F É Y)
2. Y É ~C
3. I ×
E
/ F É ~C
3)
1. L v O
2. (F v C) É B
3. L É F
4. O É
C
/ B
4)
1. K ×...

1. Construct a truth table for: (¬p ∨ (p → ¬q)) → (¬p ∨ ¬q)
2. Give a proof using logical equivalences that
(p → q) ∨ (q →
r) and (p → r)
are not logically equivalent.
3.Show using a truth table that (p →
q) and (¬q →
¬p) are logically equivalent.
4. Use the rules of inference to prove that the premise
p ∧ (p
→ ¬q) implies
the conclusion ¬q. Number each
step and give the...

Write a C++ program to demonstrate thread synchronization. Your
main function should first create a file called synch.txt. Then it
will create two separate threads, Thread-A and Thread-B. Both
threads will open synch.txt and write to it. Thread-A will write
the numbers 1 - 26 twenty times in nested for loops then exit. In
other words, print 1 - 26 over and over again on separate lines for
at least 20 times. Thread-B will write the letters A - Z...

Use the Chain Rule to find the indicated partial
derivatives.
N =
p + q
p + r
, p = u + vw, q =
v + uw, r = w + uv;
∂N
∂u
,
∂N
∂v
,
∂N
∂w
when u = 6, v = 5, w = 7

pseudocode please!!
Assignment6C: P0\/\/|\|3D. In the early 80s, hackers used to
write in an obfuscated, but mostly readable way called “leet” –
short for “elite”. In essence, it was a simple character
replacement algorithm, where a single “regular” character was
replaced by one or more “leet” characters; numbers remained the
same. Here’s one of the most readable versions: a 4 g 9 m /\\/\\ s
$ y ‘/ b B h |-| n |\\| t 7 z Z c (...

Please assess the following two arguments for
validity/invalidity using the abbreviated truth-table method.
Remember to show your work and provide an invalidating assignment
if the argument is invalid.
1. ~Q v H, ~H v K, K → ~W ∴ W ↔~Q
2.Z ↔ D, (R v L) → D, R ⋅ ~G ∴ Z

i) F o r t h e f o l l o w I n g f i n d t h e ( c o m p. E x
p.) f o u r I e r s e r i e s f o r x( t )
I I ) D r a w t h e am p &. P h a s e s p e c t r a
I I I ) T...

answer ASAP
(I ) Given the following assumptions : P is True, Q is False, R
is True
Determine the final answer for the following propositions
1) P --> Q --> ~R
2) ( ~ P <---> ~ R ) V P
3) (P V Q V ) <---> R
(II) Given the following sets
A = { 1, 3, 5, 7, 9, 19, 29 }, B = { 1, 5, 3}, C = {7, 8, 14}, D
= {7,8,...

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