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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.

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Please help me thnk you
kramer
For this question, we use the Pythagorean theorem.

a^2+b^2=c^2

We know the lengths of the legs, a and b.
a=3
b=4

Now, let's solve for the hypotenuse, c.

3^2+4^2=c^2
25=c^2

Take the positive square root.

\boxed{c=5}

Hope this helps! :)
8 0
3 years ago
Read 2 more answers
QUESTION 1 1 POINT<br> Factor: 27m3<br> 64.<br> Provide your answer below:<br> Content attribution
pickupchik [31]

Answer:

\boxed{ \bold{ \boxed{ \sf{(3m - 4)(9 {m}^{2}  + 12m + 16)}}}}

Step-by-step explanation:

\sf{27 {m}^{3}  - 64}

\dashrightarrow{ \sf{( {3m)}^{3}  -  {(4)}^{3} }}

Use the formula of a³ - b³ = ( a - b) ( a² + ab + b² )

\longrightarrow{ \sf{(3m - 4)(3 {m}^{2}  + 3m \times 4 +  {4}^{2} }})

\longrightarrow{ \sf{(3m - 4)( {9m}^{2}  + 12m + 16}})

Hope I helped!

Best regards! :D

5 0
3 years ago
Which is the most economic way to lessen electric consumption?
AysviL [449]

Answer:

1) c. Use only appliances to do the most important task in the house.

2) b. 112kwh

3) b. 111kwh

Step-by-step explanation:

Energy can be defined as the ability (capacity) to do work and it's measured in Joules. The various forms of energy are solar energy, chemical energy, thermal energy, wind energy, nuclear energy, electrical energy, etc.

Power can be defined as the energy required to do work per unit time.

Mathematically, it is given by the formula;

Power = \frac {Energy}{time}

Energy consumption is the total amount of power used by an electronic device per unit time and it's measured in Watt-hour or Kilowatt-hour.

Mathematically, it is given by the formula;

Energy = power * time

Generally, the most economic way to lessen electric consumption is by ensuring only the important electrical appliances are used at all times.

2. Given the following data;

Previous reading = 2156 KWh

Present reading = 2268 KWh

To find how many kilowatt-hour was consumed;

Energy consumption = present reading - previous reading

Energy consumption = 2268 - 2156

<em>Energy consumption = 112 KWh</em>

3. Given the following data;

Previous reading = 5512 KWh

Present reading = 5623 KWh

To find the electrical consumption of Falogme Family;

Electrical consumption = present reading - previous reading

Electrical consumption = 5623 - 5512

<em>Electrical consumption = 111 KWh</em>

6 0
3 years ago
What capacity that is more appropriate for a soup bowl,200 liters or 300 milliliters
max2010maxim [7]
300 milliliters would be more appropriate for a soup bowl  :)
5 0
3 years ago
Read 2 more answers
I don’t understand need help
RideAnS [48]

Answer: Choice D

(a-e)/f

=======================================

Explanation:

Points D and B are at locations (e,f) and (a,0) respectively.

Find the slope of line DB to get

m = (y2-y1)/(x2-x1)

m = (0-f)/(a-e)

m = -f/(a-e)

This is the slope of line DB. We want the perpendicular slope to this line. So we'll flip the fraction to get -(a-e)/f and then flip the sign from negative to positive. That leads to the final answer (a-e)/f.

Another example would be an original slope of -2/5 has a perpendicular slope of 5/2. Notice how the two slopes -2/5 and 5/2 multiply to -1. This is true of any pair of perpendicular lines where neither line is vertical.

8 0
3 years ago
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