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
Marysya12 [62]
3 years ago
8

Consider the following argument. If I get a Christmas bonus, I'll buy a stereo. If I sell my motorcycle, I'll buy a stereo. ∴ If

I get a Christmas bonus or I sell my motorcycle, then I'll buy a stereo. Let p = "if I get a Christmas bonus," q = "if I sell my motorcycle," and r = "I'll buy a stereo." Is the argument valid or invalid?
Select the answer that shows the symbolic form of the argument and justifies your conclusion. form:______.
p → r invalid, converse error
q → r
∴ p ∨ q → r
form:_____.
r → q valid, proof by division into cases
r → p
∴ r → p ∨ q
form:______.
r → q invalid, converse error
r → p
∴ r → p ∨ q
form:______.
p → r valid, proof by division into cases
q → r
∴ p ∨ q → r
form:_______.
r → q invalid, inverse error
r → p
∴ r → p ∨ q
Mathematics
1 answer:
Nuetrik [128]3 years ago
4 0

Answer:

p → r valid, proof by division into cases

q → r

∴ p ∨ q → r

Step-by-step explanation:

Let

p = "if I get a Christmas bonus,"

q = "if I sell my motorcycle,"

and

r = "I'll buy a stereo."

This can be written as:

If I get a Christmas bonus, I'll buy a stereo

p → r

If I sell my motorcycle, I'll buy a stereo

q → r

∴ If I get a Christmas bonus or I sell my motorcycle, then I'll buy a stereo.

∴ p ∨ q → r

To prove this argument we partition the argument into a group of smaller statements that together cover all of the original argument and then we prove each of the smaller statements. If you see the conclusion ∴ p ∨ q -> r so if the conclusion contains a conditional argument of form "If A1  or A2 or... or An then C ”, then we prove "If A1 then C", "If A2 then C" and so on upto "If An then C" . This depicts that the conclusion  C is true no matter which if the Ai holds true. This method is called proof by division into cases. In the given example, this takes the form:

p → r

q → r

p ∨ q

∴ r

Since proof by division into cases is an inference rule thus given argument is valid. Lets make a truth table to show if this argument is valid

p   q   r   p ∨ q   p → r    q → r    p ∨ q → r

0   0   0     0        1           1             1

0   0   1      0        0          0            0

0   1    0     1         1           0            0

0   1    1      1         0          1               1

1    0   0     1         0          1             0    

1    0   1      1         1           0            1    

1    1    0     1         0          0            0    

1    1    1      1         1           1              1    

An argument is valid if all of the premises are true, then the conclusion is true. So the truth table shows that the conclusion is true i.e. 1 where all premises are true i.e. 1. So the argument is valid.

Hence

p → r valid, proof by division into cases

q → r

∴ p ∨ q → r

You might be interested in
WILL GIVE BRAINLIEST
Rufina [12.5K]

Answer:

60

Step-by-step explanation:

rate of change of graph,df(x)/dx

=(120-0)/(3-1)=60

8 0
3 years ago
I need help on this may you help
HACTEHA [7]

Answer:

should be 63

Step-by-step explanation:

6 0
1 year ago
Kaylib’s eye-level height is 48 ft above sea level, and addison’s eye-level height is 85 and one-third ft above sea level. how m
GalinKa [24]

The addison see to the horizon at 2 root 2mi.

We have given that,Kaylib’s eye-level height is 48 ft above sea level, and addison’s eye-level height is 85 and one-third ft above sea level.

We have to find the how much farther can addison see to the horizon

<h3>Which equation we get from the given condition?</h3>

d=\sqrt{\frac{3h}{2} }

Where, we have

d- the distance they can see in thousands

h- their eye-level height in feet

For Kaylib

d=\sqrt{\frac{3\times 48}{2} }\\\\d=\sqrt{{3(24)} }\\\\\\d=\sqrt{72}\\\\d=\sqrt{36\times 2}\\\\\\d=6\sqrt{2}....(1)

For Addison h=85(1/3)

d=\sqrt{\frac{3\times 85\frac{1}{3} }{2} }\\d\sqrt{\frac{256}{2} } \\d=\sqrt{128} \\d=8\sqrt{2} .....(2)

Subtracting both distances we get

8\sqrt{2}-6\sqrt{2}  =2\sqrt{2}

Therefore, the addison see to the horizon at 2 root 2mi.

To learn more about the eye level visit:

brainly.com/question/1392973

5 0
2 years ago
Please Help!! ASAP 50 POINTS!!!!!!!!
soldier1979 [14.2K]

The statement will be m∠ABC = m∠GHI.

Reason: ∠ABC ≅ ∠GHI

4 0
3 years ago
The radius of a circle is 2 centimeters. What is the circles circumference?
Salsk061 [2.6K]

Answer: 4π cm or 12.56 cm

Step-by-step explanation: To find the circumference of this circle, start with the formula for the circumference of a circle which is C = 2πr.

Since the radius is 2 centimeters, we can

plug in 2 centimeters for <em>r</em> in the formula.

So we have (2)(π)(2 cm) which is equal to 4π cm.

So the circumference of this circle is 4π cm.

Remember that π is approximately equal to 22/7 or 3.14 so we can estimate the value of the circumference by plugging in 3.14 for π.

So we have (4)(3.14) which is equal to 12.56.

So the circumference of the circle is

approximately equal to 12.56 cm.

5 0
3 years ago
Other questions:
  • Help help helpsbnddnd
    8·2 answers
  • The perimeter of a rectangular concrete patio is 100 meters. it is 30 meters long. how wide is it?
    13·1 answer
  • 1.70f+1.30s=37.90, 5.60f+5.40=147.20
    15·2 answers
  • Please help me if so thank you
    11·1 answer
  • Please help me with trigonometry and law of sines I’m being timed and really need the help
    11·1 answer
  • Determine the singular points of the given differential equation. Classify each singular point as regular or irregular. (Enter y
    13·1 answer
  • May someone help me with this math problem?
    11·2 answers
  • Which shop is cheaper for Carmen to buy 6 cans?
    5·2 answers
  • Solve 9,159 divided by 7
    8·2 answers
  • I need help please. can someone please help me
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!