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
MariettaO [177]
3 years ago
6

Consider the following argument. If there are as many rational numbers as there are irrational numbers, then the set of all irra

tional numbers is infinite.
The set of all irrational numbers is infinite. ∴
There are as many rational numbers as there are irrational numbers. Let p = "there are as many rational numbers as there are irrational numbers," and let q = "the set of all irrational numbers is infinite."
Is the argument valid or invalid?
Choose the answer that shows the symbolic form of the argument and justifies your conclusion.
a. form: q ∧ p valid, specialization p ∴ q
b. form: p → q invalid, converse error q ∴ p
c. form: q ∧ p invalid, converse error p ∴ q
d. form: p ∨ q invalid, inverse error q ∴ p
e. form: q → p valid, generalization p ∴ q
Mathematics
1 answer:
FrozenT [24]3 years ago
6 0

Answer:

b. form: p → q invalid, converse error q ∴ p

Step-by-step explanation:

Let

p = "there are as many rational numbers as there are irrational numbers,"

let

q = "the set of all irrational numbers is infinite."

We can write the above argument as:

If there are as many rational numbers as there are irrational numbers, then the set of all irrational numbers is infinite

p → q

The set of all irrational numbers is infinite

q

There are as many rational numbers as there are irrational numbers

p

So collectively it can be written as:

p → q

 q

∴p

So it looks like

if p then q

q

therefore p

This is a fallacious argument.  This means the conclusion can be false even when the premises are true. This type of argument is invalid.

Suppose we know that “If there are as many rational numbers as there are irrational numbers, then the set of all irrational numbers is infinite” is a true conditional statement. We also know that "the set of all irrational numbers is infinite" is true. This is not enough to say that "there are as many rational numbers as there are irrational numbers," is true. The reason for this is that there is nothing logically about “If p then q” and “q” that means p must follow. So this is a converse error and since converse error is an invalid method of inference rule so this argument is invalid.

Let us prove this argument is invalid with a truth table:

p   q   p → q   q   p

T   T      T       T   T

T   F      F       F   T

F   T      T       T   F

F   F      T       F   F

Since we know that the premises are:

p → q   and  q

and the conclusion is p

and an argument is valid if and only if all of its premises are true, then the conclusion is true. We should check that whenever both p → q   and  q are true then p is true but the third row fails. Thus this is an invalid argument.

You might be interested in
Find the approximate value of b in the triangle shown.<br>13<br>12<br>8<br>5​
givi [52]

Answer:

The answer is D. 5

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Which of the following is a geometric sequence?
professor190 [17]

Answer:

A

Step-by-step explanation:

A is a geometric sequence with common ratio - 1.

5 0
3 years ago
Read 2 more answers
You have 846.82 in your bank account. How much Simple Interest will your money earn after 1 year?
vlabodo [156]

Answer:

sorry i do not know the answer to this one :(SORRY):

Step-by-step explanation:

4 0
2 years ago
Jim drives his children to their sports activities outside of school. When he drives his son to baseball practice, it is a 6-km
trapecia [35]

Answer:

17.4 kilometers per week

Step-by-step explanation:

we know that

The number of kilometers that Jim drives a week is equal to the number of baseball practice multiplied by its round trip plus the number basketball practice multiplied by its round trip

Remember that

1\ km=1,000\ m

so

1,800\ m=1,800/1,000=1.8\ km

2(6)+3(1.8)=17.4\ km

6 0
3 years ago
You have invested $5000 in stocks and bonds. The interest you earned on the stocks was 7%. The interest you earned on the bonds
Sphinxa [80]
Money invested S + B = $5000 - - - - (a)
Money earned can be represented in S & B as follows:
0.07*S + 0.14*B =$500 - - - - (b)

Equations a & b are two equations with two unknowns.

From equation a:
S = 5000 - B
Replace S in equation b
0.07*(5000 - B) + 0.14*B =$500
0.07B = 500 - 350 = $150
B = 150/0.07 = $2142.86
S = 5000 - 2142.86 = $2857.14

Good luck
8 0
3 years ago
Other questions:
  • Find a formula for a function of the form y=bxe^−ax with local maximum at (1,2.2073). y=________
    14·1 answer
  • 1/1.5 = 1/2.0 + 1/c<br><br><br><br> find c and please please show all your work
    10·1 answer
  • Segment endpoints: (0,0) and (0,20) midpoint
    10·1 answer
  • The square of the sum of 7 times x and 3 divided by 4 times the difference of x and 1
    14·1 answer
  • 4. MARKERS A student bought a box of markers. She gave 6 markers to
    9·1 answer
  • Is (1, 4) a solution to the equation y = 7x?
    10·1 answer
  • CAN YOU PLS HELP ME WITH THIS I NEED THIS NOW!! I WILL GIVE BRAINLY TO BEST ANSWER THANK YOU!!
    9·1 answer
  • This year Maya watched 60 movies. She thought that 33 of them were very good. Of the movies she watched, what percentage did she
    14·1 answer
  • For what value of k will the relation not be a function<br> R={(k-8.3+2.4k,-5),(3/4k,4)}
    8·1 answer
  • Determine how much this home would cost to replace: 3,800 square feet at $102.00 per square foot
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!