If the following statements are true, use the Law of Detachment to derive a new true statement.
1) If you are a penguin, then you live in the Southern Hemisphere.
2) You are a penguin.
Remember if p then q
The law of detachment, or modus ponens, doesn't apply when the antecedent is false or when premises lack conditional statements, making deductions invalid in these cases.
The law of detachment, also known as modus ponens, is a fundamental principle in classical logic that allows us to make valid deductions. However, there are situations where it does not apply:
Invalid Antecedent: In modus ponens, we start with a conditional statement (if-then statement) as our premise and then affirm the consequent. If the antecedent (the "if" part) of the conditional statement is false, the law of detachment cannot be applied. For example, if we have the statement "If it is raining, then the ground is wet" and we know that the ground is not wet, we cannot conclude anything about whether it's raining or not, as the antecedent is false.
Lack of a Conditional Statement: Modus ponens requires a conditional statement as its premise. If we are given unrelated or non-conditional premises, we cannot apply this rule. For instance, if we know that "John is a doctor" and "The sun is shining," we cannot use modus ponens to deduce anything because there is no conditional relationship between the statements.
In summary, while modus ponens is a valid and powerful inference rule in classical logic, it cannot be applied when the antecedent is false or when the premises do not involve conditional statements.
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Complete question below:
Could you provide two examples where the law of detachment does not apply in logic?
PLEASE HELP WITH SOME GEOMETRY
Prove the following statement by contradiction using an indirect proof. In a triangle angle A = 90°, then the triangle is a right triangle. Which of the following choices would be the first step to temporarily assume?
angle A = 90°
the triangle is a right triangle
the triangle is not a right triangle
angle A is not 90°
How can I use context clues and keywords to translate situations into inequalities? Explain with an example of your own.
To translate situations into inequalities, use context clues and keywords. Start by understanding the relationships and factors involved. Then, represent the situation with variables and create an inequality based on the context clues. For example, if Bob earns $10 more than Alice, the inequality would be 'a < a + 10'.
Explanation:In order to use context clues and keywords to translate situations into inequalities, it's important to understand the relationships and factors involved. Let's take an example:
Scenario: Suppose you have two friends, Bob and Alice. Bob earns $10 per hour more than Alice. In this case, we can use the following context clues:
The relationship between Bob and Alice: Their wealth is unequal.The factor involved: The difference in their earnings.We can now translate this situation into an inequality:
Let's say Alice's earnings are represented by 'a'.Bob's earnings would be 'a + 10' (since he earns $10 more).The inequality can be represented as 'a < a + 10' (Alice's earnings are less than Bob's earnings).By using the context clues and the keywords (earnings, difference), we were able to translate the situation into the inequality 'a < a + 10'.
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Pick the correct description of the line 5x + 3y=15
Answer:
The correct description is [tex]y=5-\frac{5x}{3}[/tex]
Step-by-step explanation:
In this case, firts we have to organize the equation in the normal way, where y is alone in one side, this is:
[tex]5x+3y=15\\3y=15-5x\\y=\frac{15}{3}-\frac{5x}{3} \\y=5-\frac{5x}{3}[/tex]
The correct description is [tex]y=5-\frac{5x}{3}[/tex]
Now we can see that the slope of the equation is [tex]-\frac{5}{3}[/tex]
What's the next value?
1 I 2 L 3 F 4
Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) −1 s (s − 5)(s − 6)(s − 30)
2/3 of a number is 32, what is the number?
Name the three different types of proof in math and give a description of each
A pharmacist has 40% and 80% iodine solutions on hand .How many liters of each iodine solutions will be required to produce 6 liters of a 50% iodine mixture?
let f(x)=4x-1 and g(x)=2x^2+3. perform the function operation and then find the domain. To
f(x) + g(x)
HELP!! A spherical ball just fits inside a cylindrical can, 16 centimeters tall, with a diameter of 16 centimeters. Which expression gives the volume of the sphere in cubic centimeters?
formula for volume of a sphere is V=4/3 x pi x R63
if diameter = 16 than radius = 16/2 = 8
so the equation would be 4/3 x pi x 8^3
On average, Donna's Cafe has 18 customers, which represents 36% of the total approved occupancy by the fire department. a. What is the total approved occupancy of the cafe by the fire department? Total approved occupancy = customers b. According to the fire department's occupancy approval, what percentage of the cafe is still available for customers? Available occupancy percentage = % c. According to the fire department's occupancy approval, how many seats are still available for customers? Seats still available =
amy has 72 sweets in bag.she keeps 1/4 of them for herself,but shares the remainder between 6 of her friends.how many sweets will she give to each of her friends?
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the second equation is substituted into the first equation.
2x – 7y = 4
3x + y = –17
Which quantity is proportional to 20/5?
0.025 in scientific notation (step by step)
0.025 in scientific notation is 2.5 × 10⁻².
To express 0.025 in scientific notation, we need to convert the decimal form to a number multiplied by a power of 10.
Here's how you can do it step by step:
Start with the given decimal number: 0.025.
Identify the non-zero digit. In this case, it is 2.
Move the decimal point to the right until there is only one non-zero digit to the left of the decimal point. Count the number of places you moved the decimal point. In this case, we moved the decimal point two places to the right.
0.025 -> 2.5
Write the non-zero digit (2.5) as a decimal number.
Finally, express the power of 10 that represents the number of places you moved the decimal point. Since we moved the decimal point two places to the right, the power of 10 is -2.
Putting it all together, we have:
0.025 = 2.5 × 10⁻²
Therefore, 0.025 in scientific notation is 2.5 × 10⁻².
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How to solve 7.86 x 4.6
jim sold 200 litters of soda at baseball game.How much is this in milliters?
A study of sleep patterns randomly selected participants in the study to sleep in either a dark room or a room with light.
Which element of experiment design is known to be a part of this study?
A.
blinding
B.
replication
C.
randomization
Answer:
C. randomization
Step-by-step explanation:
We are told that the study randomly selects participants in the study to sleep in either a dark room or a room with light. This means that randomization is part of the study.
Madison deposited a total of $5,000 between two saving accounts bearing simple interest. One of the accounts has an interest rate of 4% while the other rate is 5%. If the total interest earned after one year is $220, find the amount deposited into each of the accounts.
What is the difference of the polynomials?
(8r6s3 – 9r5s4 + 3r4s5) – (2r4s5 – 5r3s6 – 4r5s4)
Answer: The required difference is [tex]8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6.[/tex]
Step-by-step explanation: We are given to find the difference of the polynomials as follows :
[tex]DP=(8r^6s^3-9r^5s^4+3r^4s^5)-(2r^4s^5-5r^3s^6-4r^5s^4)~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the given difference, we need to choose the terms with same poers of the unknown variables r and s and then subtract their coefficients.
The difference (i) is as follows :
[tex]DP\\\\=(8r^6s^3-9r^5s^4+3r^4s^5)-(2r^4s^5-5r^3s^6-4r^5s^4)\\\\=8r^6s^3-9r^5s^4+3r^4s^5-2r^4s^5+5r^3s^6+4r^5s^4\\\\=8r^6s^3+(4-9)r^5s^4+(3-2)r^4s^5+5r^3s^6\\\\=8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6.[/tex]
Thus, the required difference is [tex]8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6.[/tex]
If prices Increase at a monthly rate of 2.3%, by what percentage do they increase in a year?
A company uses a variable percentage markup of 35% .if the total cost of a product is $15,what is its selling price
The selling price of a product with a 35% markup on a cost of $15 is calculated by adding the markup amount of $5.25 to the cost, resulting in a selling price of $20.25.
Explanation:To calculate the selling price of a product using a variable percentage markup, you first need to determine the amount of markup by converting the percentage to a decimal and multiplying by the cost of the product. In this case, with a 35% markup on a product that costs $15, the calculation is as follows:
$15 × 0.35 = $5.25
This $5.25 represents the amount of markup on the product. To find the selling price, you simply add the markup to the cost:
$15 + $5.25 = $20.25
Therefore, the selling price of the product would be $20.25.
4 students equally share 3/4 of a pizza. How much of the pizza does each student get?
To find out how much pizza each of 4 students gets when they equally share 3/4 of a pizza, we divide the amount of pizza (3/4) by the number of students (4). The result is 3/16, which means each student gets 3/16 of the pizza.
Explanation:The question asks how 4 students can equally share 3/4 of a pizza. In mathematics, to divide a quantity equally amongst a group, we perform division. So, in this scenario, we need to divide 3/4 (the pizza) by 4 (the students).
Step 1: Represent the given scenario as a division problem: 3/4 ÷ 4. Step 2: Convert the division into multiplication by the reciprocal. This changes our problem into a multiplication problem: 3/4 * 1/4. Step 3: Multiply the numerators together to get the numerator of the answer: 3 * 1 = 3. Step 4: Multiply the denominators together to get the denominator of the answer: 4 * 4 = 16.
So, the answer of 3/4 ÷ 4 is equal to 3/16. Therefore, each student gets 3/16 of the pizza.
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An apple farmer has planted 0.3 of his orchard with cherry trees. The orchard is 8.59 acres in size. How many acres are planted with cherry trees
Find the area under the standard normal curve between z = −2.57 and z = 1.27. Round your answer to four decimal places, if necessary.
The area under the standard normal curve between z = −2.57 and z = 1.27 is, 0.8929
What is meant by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We have to give that,
To find the area under the standard normal curve between z = −2.57 and z = 1.27.
Now, the area under the standard normal curve is between z = −2.57 and z = 1.27 is,
P(-2.57 ≤ Z ≤ 1.27) = P(Z ≤ 1.27) - P(Z ≤ -2.57)
Since, P(Z ≤ 1.27) = 0.8980
And, P(Z ≤ -2.57) = 1 - P(Z ≤ 2.57)
= 1 - 0.99488
= 0.00512
Hence,
P(-2.57 ≤ Z ≤ 1.27) = 0.8980 - 0.00512
= 0.89288
= 0.8929
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Find the area of a triangle with legs that are: 15mm,10mm,20mm
The area of a triangle with legs that are 15 mm, 10 mm, and 20 mm is [tex]72.618 mm^{2}[/tex]
Further Explanation;Area Area is a measure of how much space is occupied by a given shape. Area of a substance is determined by the type of shape in question.For example;
Area of a rectangle is given by; Length multiplied by width Area of a circle = πr². where r is the radius of a circle, Area of a square = S², Where s is the side of the square.etc.Area of a triangle The area of a triangle is given based on the type of the triangle in question.Right triangle.The area of a right triangle is given by;= 1/2 x base x height
Scalene triangleIt is a triangle that with sides and angles that are not equal.Area of a scalene triangle depends on the features of the triangle given.For example;
Sine FormulaArea of a triangle = 1/2 ab sin θ, when given two sides of the triangle and the angle between themHeron's formulaArea of a triangle = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex] when given all the sides of the triangle. where [tex]s =\frac{(a+b+c)}{2}[/tex]In this case we are given, a = 15 mm, b = 10 mm, c = 20 mm
Therefore, we use the Heron's formula;
Area= [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]s =\frac{(a+b+c)}{2}[/tex]
[tex]s= \frac{(15+10+20)}{2} \\s= 22.5[/tex]
Therefore;
Area = [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex]
= [tex]22.5\sqrt{22.5(22.5-15)(22.5-10)(22.5-20)}[/tex]
=[tex]\sqrt{22.5(7.5)(12.5)(2.5)} \\\sqrt{5273.4375}[/tex]
[tex]= 72.618 mm^{2}[/tex]
Keywords: Area, Area of a triangle, Heron's formula, Sine formula, Scalene triangle.
Learn more about: Perimeter: https://brainly.com/question/12905000 Area: https://brainly.com/question/12905000 Area of a triangle: https://brainly.com/question/4125306Heron's Formula: https://brainly.com/question/10713495Level: Middle school
Subject; Mathematics
Topic: Area
Sub-topic: Area of a triangle
True or false: the difference between the lower limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error.
an actor gains 20pounds for a part and then losses 15 pounds during the filming of the movie to go along with the story.who do you write a addition expression to describe this situation
Convert decimal +49 and +29 to binary, using the signed‐2’s‐complement representation and enough digits to accommodate the numbers. then perform the binary equivalent of (+29) + (-49), (-29) + (+49), and (-29) + (-49). convert the answers back to decimal and verify that they are correct.
To solve this problem, let us first find for the binary equivalents of the numbers. They are:
Decimal --> Binary
+ 29 --> 00011101
+ 49 --> 00110001
- 29 --> 11100011
- 49 --> 11001111
Now we apply the normal binary arithmetic to these converted numbers:
(+ 29) + (- 49) ---> 00011101 + 11001111 = 11101100 ---> - 20 (TRUE)
(- 29) + (+ 49) ---> 11100011 + 00110001 = 00010100 ---> + 20 (TRUE)
(- 29) + (- 49) ---> 11100011 + 11001111 = 10110010 ---> - 78 (TRUE)
which algebraic expression represents the phase