1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ki77a [65]
3 years ago
14

1. Consider the following hypotheses:

Mathematics
1 answer:
Andrej [43]3 years ago
7 0

Answer:

See deductions below

Step-by-step explanation:

1)

a) p(y)∧q(y) for some y (Existencial instantiation to H1)

b) q(y) for some y (Simplification of a))

c) q(y) → r(y) for all y (Universal instatiation to H2)

d) r(y) for some y (Modus Ponens using b and c)

e) p(y) for some y (Simplification of a)

f) p(y)∧r(y) for some y (Conjunction of d) and e))

g) ∃x (p(x) ∧ r(x)) (Existencial generalization of f)

2)

a) ¬C(x) → ¬A(x) for all x (Universal instatiation of H1)

b) A(x) for some x (Existencial instatiation of H3)

c) ¬(¬C(x)) for some x (Modus Tollens using a and b)

d) C(x) for some x (Double negation of c)

e) A(x) → ∀y B(y) for all x (Universal instantiation of H2)

f)  ∀y B(y) (Modus ponens using b and e)

g) B(y) for all y (Universal instantiation of f)

h) B(x)∧C(x) for some x (Conjunction of g and d, selecting y=x on g)

i) ∃x (B(x) ∧ C(x)) (Existencial generalization of h)

3) We will prove that this formula leads to a contradiction.

a) ∀y (P (x, y) ↔ ¬P (y, y)) for some x (Existencial instatiation of hypothesis)

b) P (x, y) ↔ ¬P (y, y) for some x, and for all y (Universal instantiation of a)

c) P (x, x) ↔ ¬P (x, x) (Take y=x in b)

But c) is a contradiction (for example, using truth tables). Hence the formula is not satisfiable.

You might be interested in
To solve the formula M = 2P + 3Q for the variable Q
PolarNik [594]
Q=M-2P/3

because in order to solve for a variable you have to get alone. Make sense?
7 0
2 years ago
Read 2 more answers
Which graph models the function f(x) = −2(3)x?
swat32

Answer:

exponential function going through point 0, negative 2 and ending down on the right

Step-by-step explanation:

(Took the test, also seen as "Option A", this graph goes down and hits the y line at 0,-2.)

6 0
3 years ago
What is 44 divided by 93
Shalnov [3]

Answer:

0.47311827957

Step-by-step explanation:

44/93= 0.47311827957

hope this helps u

5 0
3 years ago
John and Samuel had a challenge. John told Samuel that 12 x 12=9. What strategy did John use to come up with his answer as 9? Ex
kondor19780726 [428]

Answer:

John added 1 +4 +4 to get 9 (12x12 = 144)

Step-by-step explanation:

12x12 actually equals 144

1 + 4 +4 = 9 so it appears John just added all the digits of 144 to get 9

8 0
3 years ago
Please help !!! Number 11
romanna [79]

Answer:

C) 153.9 in²

Step-by-step explanation:

14 ÷ 2 = 7

π = 3.14

3.14×7×7 = 153.9 in²

hope this helps!

5 0
3 years ago
Read 2 more answers
Other questions:
  • Which facts are true for the graph of the function below? Check all that apply. F(x) = log6 x
    13·2 answers
  • What is -2 - 5/4x=30
    7·1 answer
  • If a/4=2, what does a equal
    5·1 answer
  • Below is a piece of a local pizza place menu where Jacob works.
    13·1 answer
  • Write a system of equations modeling the given conditions. Then solve the system by the substitution method and find the two num
    14·1 answer
  • Three lines intersect to form the triangle shown below. What is the value of x in degrees?
    6·1 answer
  • Pls help i will mark brainliest
    6·2 answers
  • What is the equation of a line that is parallel to the x-axis and is 3 units below the x-axis
    9·1 answer
  • PLEASE HELP ANSWER THIS QUESTION!!!
    8·2 answers
  • Which survey question could have been asked to produce this data display?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!