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Stells [14]
3 years ago
12

Which of the following are valid (necessarily true) sentences? a. (∃x x = x) ⇒ (∀ y ∃z y = z). b. ∀ x P(x) ∨ ¬P(x). c. ∀ x Smart

(x) ∨ (x = x)
Mathematics
1 answer:
Phantasy [73]3 years ago
7 0

Answer:

b; ∀x   P(x) ∨ ¬P(x)

Step-by-step explanation:

Suppose that we have a proposition p

Such that p can be true or false.

We can define the negation of p as:

¬p

Such that, if p is false, then ¬p is true

if p is true, then ¬p is false.

Also remember that a proposition like:

p ∨ q

is true when, at least one, p or q, is true.

Then if we write:

p ∨ ¬p

Always one of these will be true (and the other false)

Then the statement is true.

And if the statement depends on some variable, then we will have that:

p(x) ∨ ¬p(x)

is true for all the allowed values of x.

from this, we can conclude that the statement that is always true is:

b; ∀x   P(x) ∨ ¬P(x)

Where here we have:

For all the values of x,   P(x)  ∨ ¬P(x)

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Answer:

a) 0.283  or 28.3%

b) 0.130 or 13%

c) 0.4 or 40%

d) 30.6 mm

Step-by-step explanation:

z-score of a single left atrial diameter value of healthy children can be calculated as:

z=\frac{X-M}{s} where

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Then

a) proportion of healthy children who have left atrial diameters less than 24 mm

=P(z<z*) where z* is the z-score of 24 mm

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And P(z<−0.574)=0.283

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= P(z>z*) = 1-P(z<z*) where z* is the z-score of 32 mm

z*=\frac{32-26.7}{4.7} ≈ 1.128

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z(30)=\frac{30-26.7}{4.7} ≈ 0.702

z(25)=\frac{25-26.7}{4.7} ≈ −0.362

P(z<0.702)=0.7587

P(z<−0.362)=0.3587

Then P(z(25)<z<z(30)) =0.7587 - 0.3587 =0.4

d) to find the value for which only about 20% have a larger left atrial diameter, we assume

P(z>z*)=0.2 or 20% where z* is the z-score of the value we are looking for.

Then P(z<z*)=0.8 and z*=0.84. That is

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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So, one side of the field is 12m; now we just find the perimeter which is easy since its a square. 12*4=48m

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Answer:

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Step-by-step explanation:

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-6x         -6x

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y = -6/4x + 18

perpidicular slope is the opposite reciprical of the original line:

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4/6  or 2/3 would be the desired slope

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