Form The Converse Of The Following Proposition: All A Are B ✓ Solved
Form the Converse of the following proposition. All A are B.
1. Form the Converse of the following proposition: All A are B.
2. Form the Obverse of the following proposition: No A are B.
3. Form the Contrapositive of the following propositions: Some A are B, and Some A are not B.
4. An 'Immediate Inference.' If I have an argument and the premise is No A are B, and the Conclusion is No Non-B are non-A, is it valid or invalid? Look at the Venn Diagrams. Draw them here if it is possible on Moodle.
5. This will be a bonus question because I think it's hard. It involves higher order thinking, or "meta" thinking, or interpretation. We said earlier that the 'term compliment' of a term was that which denotes all things in the world not denoted by the original term. So if Oak trees is a category, denoted by O, then all things not oak trees is denoted by non-O, its term compliment. Why is this valuable information?
Paper For Above Instructions
The study of propositions and their inferential relationships forms the backbone of logical reasoning. Understanding the logical forms such as converse, obverse, contrapositive, and the truths of arguments is crucial for critical thinking. Below, we will explore the details of each question while applying the appropriate logical frameworks.
1. Converse of a Proposition
The converse of a proposition is formed by reversing the subject and predicate. For the proposition "All A are B," the converse would be "All B are A." It’s essential to understand that the truth of the original proposition does not guarantee the truth of its converse. For example, while it is true that "All squares are rectangles," it does not logically follow that "All rectangles are squares." This illustrates the fundamental distinction in logical relations.
2. Obverse of a Proposition
The obverse of a proposition involves negating the predicate and changing the quality of the statement. Therefore, for the proposition "No A are B," the obverse would be "All A are non-B." This transformation maintains the same truth value: if no A are B is true, then it follows that all A cannot be anything but non-B.
3. Contrapositive of a Proposition
The contrapositive of a proposition switches and negates both the subject and predicate. For "Some A are B," the contrapositive is "Some non-B are non-A." Similarly, for "Some A are not B," the contrapositive is "Some non-A are not non-B." The significance of the contrapositive is that it holds the same truth value as the original proposition—a cornerstone in proving the validity of syllogistic arguments.
4. Validity of Immediate Inference
Analyzing the argument where "No A are B" serves as the premise and "No Non-B are non-A" as the conclusion, we resort to Venn Diagrams for visual aid. In this case, if no A can exist within B, it logically follows that the non-existence of B implies non-existence of A. Hence, the conclusion validly represents the argument. As visualized in a Venn Diagram, the circles of A and B do not overlap, solidifying the argument's indecomposable nature.
5. The Value of Term Complement
Understanding term complement—where "O" represents Oak trees and "non-O" represents everything that is not an Oak tree—offers profound insights. Such classification aids not only in logical deduction but also in categorical understanding. The prominence of this terminology in logic facilitates clarity in discourse and reasoning, particularly in fields like philosophy, linguistics, and mathematics. Recognizing what 'non-O' includes helps in articulating exclusions, which are crucial for both ethical reasoning and scientific inquiries.
Combining Theory with Practical Application
Having established the theoretical framework, practical understanding can be drawn from these concepts through applications in real-life scenarios. Using propositions to analyze financial decisions, such as contemplating relocating for a job, confirms how logical inferences can illuminate one’s understanding of economic parameters.
International Compensation and Taxation Considerations
In choosing a dream job abroad, let's assess two possible roles: an HR consultant in Vancouver, Canada, and an HR consultant in Los Angeles, USA. For estimation, consider the average yearly salary of HR consultants in Canada and the USA. Suppose it is approximately CAD 75,000 in Canada and USD 70,000 in the USA. This conversion leads us to calculate the Canadian equivalent of that US salary.
Utilizing an exchange rate of around 1.3 for USD to CAD, the average salary in LA would be approximately CAD 91,000 (USD 70,000 * 1.3). Next, we consider taxation rates. For Canadian taxation, let’s say 25-30% of earnings are taxed, amounting to CAD 18,750 - 22,500 deducted from the gross salary. For the USA, a similar tax bracket may range around 22-28%, suggesting approximately CAD 20,020 - 25,480 for taxes deducted.
To accurately calculate cost of living adjustments (COLA), we juxtapose cities like Vancouver and Los Angeles. Using various economic indicators, including housing, transportation, and overall living expenses—say, the average living costs in Vancouver are estimated at CAD 2,500 monthly (CAD 30,000 annually), while in Los Angeles, it sits around CAD 3,200 monthly (CAD 38,400 annually)
Finally, calculating earnings after taxes, and expenses uncovers actual savings. For Vancouver: CAD 75,000 - 22,500 - 30,000, translates to CAD 22,500 savings. In Los Angeles: CAD 91,000 - 25,480 - 38,400 reflects only CAD 27,120 remaining. With these calculations, one can weigh the benefits illuminating which path is most financially viable.
Conclusion
Deciding whether to emigrate or stay put often relies on economic justifications. Given the classification of possible earnings, taxes, and cost of living comparisons, one could conclude that despite higher post-tax savings in Los Angeles, the sustainable quality of life and work-related stress in Canada provides more substantial benefits. Therefore, upon this analytical evaluation, while the dream of moving to the USA is indeed alluring, the reality shows that staying in Canada yields a better balance of happiness over material wealth, making it a more prudent choice.
References
- American Payroll Association. (2023). "Guide to Payroll Taxes." Retrieved from [website link]
- Canada Revenue Agency. (2023). "Income Tax Rates." Retrieved from [website link]
- Government of Canada. (2023). "Canada's Cost of Living Trends." Retrieved from [website link]
- Investopedia. (2023). "Understanding COLA Adjustments." Retrieved from [website link]
- OECD. (2023). "Average Salary by Country." Retrieved from [website link]
- Statista. (2023). "Average Salary in Canada." Retrieved from [website link]
- Trading Economics. (2023). "Currency Converter: CAD to USD." Retrieved from [website link]
- U.S. Bureau of Labor Statistics. (2023). "Employment Statistics." Retrieved from [website link]
- World Population Review. (2023). "Cost of Living Comparison." Retrieved from [website link]
- Yahoo Finance. (2023). "Personal Finance and Taxation Insights." Retrieved from [website link]