Use symbols to write the logical form of each argument in, and then use a truth table to test the argument for validity. Indicate which columns represent the premises and which represent the conclusion, and include a few words of explanation showing that you understand the meaning of validity.
Exercise
Oleg is a math major or Oleg is an economics major.
If Oleg is a math major, then Oleg is required to take Math 362.
∴Oleg is an economics major or Oleg is not required to take Math 362.

Answers

Answer 1

The logical form of the given argument: Given statements: Oleg is a math major or Oleg is an economics major. If Oleg is a math major, then Oleg is required to take Math 362.Conclusion: Oleg is an economics major or Oleg is not required to take Math 362.

Let's symbolize the statements: P: Oleg is a math majorQ: Oleg is an economics majorR: Oleg is required to take Math 362The given argument can be rewritten as:P v Q(If P, then R)Therefore, Q v ~RWhere v means or, ~ means not and P v Q is the disjunction of P and Q. A truth table can be drawn to test the argument for validity:The columns that represent the premises are P and (P → R), and the column that represents the conclusion is Q v ~R. An argument is valid if and only if the conclusion is true whenever the premises are true.

Here, it can be seen that the conclusion is true in every row where the premises are true. Therefore, the given argument is valid.

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Related Questions

Data modelling is the process of documenting a software system design as an easy-to-understand diagram. Data modelling allows you to conceptually represent the data and the association between data objects and rules.
2.1 Elaborate on FIVE (5) primary goals of data modelling in software design
2.2 Following from question 2.1, elaborate on any FIVE (5) advantages of implementing data models in software design.

Answers

Data modelling is the process of documenting a software system design as an easy-to-understand diagram. Data modelling allows you to conceptually represent the data and the association between data objects and rules.

The five primary goals of data modelling in software design include the following: 1. Organizing complex data structures into simpler models.2. Eliminating data redundancy.3. Ensuring data accuracy and consistency.4. Providing an efficient data processing mechanism.5. Enhancing data security.

The five advantages of implementing data models in software design are as follows:1. Clarity: Data models help to make the system's structure easier to understand by providing a clear representation of the data.2. Standardization: Data models enable you to standardize the way data is stored, processed, and accessed, ensuring consistency across the system.3. Data Integrity: Data models ensure that data is accurate, complete, and up-to-date, improving data quality and reliability.4. Efficiency: Data models enable you to optimize data processing, which can improve system performance and responsiveness.5. Flexibility: Data models allow you to add, modify, and delete data objects and rules, making it easier to adapt to changing business requirements.

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The solution of deadlock usually use two methods: (9) ___ and (10) ____ A) Withdraw process B) Resource preemption
C) Refuse allocation of new resource D) Execute security computation

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. Cloudy Corporation has provided the following cost data for last year when 50,000 units were produced and sold: All costs are variable except for $100,000 of manufacturing overhead and $100,000 of selling and administrative expense. If the selling price is $12 per unit, the net operating income from producing and selling 120,000 units would be: 17. Constance Company sells two products, as follows: Fixed expenses total $450,000 annually. The expected sales mix in units is 60% for Product Y and 40% for Product Z. How much is Constance Company's expected break-even sales in dollars?

Answers

Constance Company's expected break-even sales in dollars are $2,160,000.

1. Net operating income from producing and selling 120,000 units would be:Given data: Selling price per unit = $12Variable costs = $8 per unitFixed manufacturing overhead = $100,000Fixed selling and administrative expense = $100,000Total cost per unit = Variable cost per unit + Fixed manufacturing overhead / Units produced= $8 + $100,000 / 50,000= $10 per unitContribution margin per unit = Selling price per unit - Total cost per unit= $12 - $10= $2 per unitContribution margin ratio = Contribution margin per unit / Selling price per unit= $2 / $12= 0.167 or 16.7%Net operating income (NOI) for 50,000 units sold= Selling price per unit × Units sold - Total cost= $12 × 50,000 - ($8 × 50,000 + $100,000 + $100,000)= $600,000 - $600,000= $0 NOI for 120,000 units sold= Selling price per unit × Units sold - Total cost= $12 × 120,000 - ($8 × 120,000 + $100,000 + $100,000)= $1,440,000 - $1,460,000= ($20,000) or a net loss of $20,000.2. Constance Company's expected break-even sales in dollars can be calculated as follows:Constance Company sells two products, Y and Z.Fixed expenses = $450,000 per yearSelling price of Product Y = $120 per unitVariable cost of Product Y = $90 per unitSelling price of Product Z = $180 per unitVariable cost of Product Z = $150 per unitContribution margin of Product Y = Selling price of Product Y - Variable cost of Product Y= $120 - $90= $30Contribution margin of Product Z = Selling price of Product Z - Variable cost of Product Z= $180 - $150= $30Weighted average contribution margin per unit = (Contribution margin of Product Y × Sales mix of Product Y) + (Contribution margin of Product Z × Sales mix of Product Z) = ($30 × 60%) + ($30 × 40%)= $18 + $12= $30Contribution margin ratio = Weighted average contribution margin per unit / Selling price per unit= $30 / [(60% × $120) + (40% × $180)]= $30 / ($72 + $72)= $30 / $144= 0.2083 or 20.83%Breakeven sales in units = Fixed expenses / Contribution margin per unit= $450,000 / $30= 15,000Breakeven sales in dollars = Breakeven sales in units × Selling price per unit= 15,000 × [(60% × $120) + (40% × $180)]= 15,000 × ($72 + $72)= 15,000 × $144= $2,160,000.

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Can get explantion of the code to better understand it
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import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report, accuracy_score
data = pd.read_csv('creditcard.csv')
data.head()
# "Time" column is the time difference from current transaction and first transaction in the database
# "Amount" column is the amount that was transacted
# Columns "V1" to "V28" are a result of PCA
# checking missing values
data.isna().sum()
# There are no missing values
# Normalizing the "Amount" values
data['Amount'] = (data['Amount'] - data['Amount'].min()) / (data['Amount'].max() - data['Amount'].min())
data.head()
# Checking correlation of features with target "Class"
plt.figure(figsize=(12, 6))
data.corr()['Class'].plot(kind='bar')
plt.show()
# Specifying training variables and target variables
X = data.drop(['Class'], axis=1).to_numpy()
y = data['Class'].to_numpy()
# Setting random seed
np.random.seed(0)
# Splitting the data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.75)
X_train.shape, X_test.shape, y_train.shape, y_test.shape
# Creating Logistic Regression classifier and training ("max_iter=1500" ensures that the model converges to the global minima)
clf = LogisticRegression(max_iter=1500)
clf.fit(X_train, y_train)
# Model accuracy on train and test sets
preds = clf.predict(X_train)
print("Training accuracy =", accuracy_score(preds, y_train))
preds = clf.predict(X_test)
print("Testing accuracy =", accuracy_score(preds, y_test))
# The classification report including precision and recall on the testing set
print(classification_report(preds, y_test))

Answers

Here is the main answer, where we will be discussing the above code and what it is doing:1) The given code is reading a CSV file named "creditcard.csv" and storing it in a Pandas Data Frame called "data". Then it is displaying the first 5 rows of the Data Frame using the head() function.2) It is then checking whether there are any missing values in the Data Frame using the isna() function and summing them.

It confirms that there are no missing values in the DataFrame.3) Then, it normalizes the values of the "Amount" column in the Data Frame. Normalization of the "Amount" column helps in getting rid of any irregularities in the data.4) A bar plot of the correlation between features and target "Class" is created using the correlation matrix of the DataFrame.5) The training and testing data are split using the train_test_split() function from sklearn.model_selection.

It returns 4 arrays, "X_train", "X_test", "y_train", and "y_test".6) A logistic regression classifier is created and fitted on the training data using the Logistic Regression() function from sklearn.linear_model.7) The predictions are generated on the training and testing data using the predict() method of the classifier. Then it is calculating and printing the training accuracy, testing accuracy and the classification report of the model. So, this is what the given code is doing in detail.

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