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MTH 154 Quantitative Reasoning Final
Logic - is the study of the methods and principles of reasoning An Argument - uses a set of facts or assumptions, called Premises and Conclusions a Fallacy - a deceptive argument in which the conclusion is not well supported by the premise Cause - Premise = Effect - Conclusion = Appeal to popularity - Many people believe P is true; therefore P is true False Cause - A came before B; Therefore A causes B Appeal to Ignorance - There is no proof that P is true; therefore P is false Hasty Generalization - A and B are linked once or a few times; therefore A caused B (or vice versa) Limited choice -
P is false; therefore only P can be true Appeal to emotion - P is associated with a positive emotional response; therefore P is true Personal Attack - I have a problem with the person or group claiming P; therefore O is not true. Circular Reasoning - P is true. P is restated in different words. (the argument starts the conclusion) Diversion (Red Herring) - P is related to Q and I have an argument concerning Q; therefore P is true Straw Man - I have an argument concerning a distorted version of P; therefore I hope you are fooled into thinking I have an argument concerning the real version of P Evaluating Media Information -
- Consider the source
- Check the date
- Validate Accuracy
- Watch for hidden Agendas
- Don't Miss the Big Picture Double Negation - "not not P" must therefore have the same truth value as the original proposition "P" Example of Double Negation - "it's unlikely that there s no association"
Given two propositions P and Q, the statement IF P, THEN Q is called their... Example of a Conditional - "If I have a voice, then I can sing" P / Q / P AND Q T / T / T T / F / F F / T / F F / F / F - Draw the truth table for P AND Q P / Q / P OR Q T / T / T T / F / T F / T / T F / F / F - Draw the truth table for P OR Q P / Q / IF P THEN Q T / T / T T / F / F F / T / T F / F / T - Draw the truth table for IF P THEN Q If... then Converse - "If Jose owns a convertible, then he owns a car." If... then inverse - "If Jose does not own a car, then he does not own a convertible"
If... then Contrapositive - "If Jose does not own a convertible, then he does not own a car" Pairs of Propositions that are logically equivalent - Conditional and Contrapositive Converse and Inverse Bi - Conditional Statement - The one that we hear, the one that parents use but don't actually say P / Q / P <->Q T / T / T T / F / F F / T / F F / F / T - Draw a bi conditional truth table Logical Equivalent - "If a creature is a whale, then it is a mammal." Example of Converse - "If it's a mammal, then the creature is a whale" Example of Inverse - "If the creature is not wale, then it's not a mammal" Example of Contrapositive - "If it's not a mammal, then the creature is not a whale" a set -
requires both true premises and validity Deductive argument - an argument that is intended by the arguer to provide a guarantee of the truth of the conclusion provided that the argument's premises are true specific conclusions - General Premises leads to (HINT: Deductive argument) valid - The argument s ____ if it's conclusion follows necessarily from it's premises, regardless of the truth of the premises or conclusions. sound - The Argument is _____ if it's valid and it's premises are true. (subtle) conclusion - An inductive argument cannot prove it's __________ true Logical structures - Validity concerns only ________________ Affirming the Hypothesis - What kind of Basic Conditional If... then statements is this: IF P, THEN Q P is true.
Valid Q is true Affirming the conclusion -
What kind of Basic Conditional If... then statement is this: IF P, THEN Q Q is true
Invalid P is true Denying the Hypothesis - What kind of Basic conditional If... then statement is this: IF P, THEN Q P is not true
Invalid Q is not true Denying the conclusion - What kind of Basic Conditional If... then statements is this: IF P THEN Q Q is not true
Valid P is not true Critical thinking n everyday life - 1. Always read or listen carefully 2.Look for the hidden meaning
- Identify the real issue
- Understand the options
- Watch for fine point and missing information
- Are other conclusions possible?
- Don't miss the big picture
C=(F-32)/1.8 -
What is the formula for Fahrenheit to Celsius? K = C + 273.15 - What is the formula for Celsius for Kelvin? K + 273.15 - What is the formula for Kelvin to Celsius? Energy - ______ is what makes matters move or heat up Power - _______ is the rate of which energy is used. Scientific Notation - a format in which a number is expressed as a number between 1 and 10 multiplied by a power of 10 Problem Solving Hints - HINT 1: There may be more than one answer HINT 2: There may be more than one method HINT 3: Use Appropriate tools HINT 4: Consider simpler, similar problems HINT 5: Consider Equivalent problems with simpler solution HINT 6: Approximations can be useful HINT 7: Try alternative patterns of thoughts Amount of increase / Original amount - What is the formula for percentage increase?
new value - reference value - What is the formula for absolute change? New value - reference value /reference value - What is the formula for relative change? decreased. - Negative values means the value has ________ more than - If the new or compared value is P% ___________ the reference value, it is (100 + P)% of the reference value Absolute difference - the actual difference between the compared value and the reference value compared value - reference value - What is the formula for absolute difference? absolute error - The __________ describes how far a measured (or claimed) value lies from the true value relative error - The ____________ compares the size of the relative error to the true value and is often expressed as a percentage Relative difference - describes the size of the absolute difference as a fraction of the reference value Absolute difference / reference value - What is the formula for relative difference?
less than - If the ___________ is less than the reference value (100 - P) instead of (100 + P). Order of Magnitude - estimate specifics of a broad range of values, usually within one or two powers of ten Random events - occurs because of random and inherently unpredictable events in the measurement process Systematic errors - occurs when there is a problem in the measurement system that affects all measurements in the same way Absolute error - describes how for a measured (or claimed) value lies from the true value measured value - true value - what is the formula for absolute error? Relative error - compares the size of the error to the truth value Absolute error / true value - what is the formula for relative error measured value - true value / true value x 100% - another possible formula for relative error? accuracy - Describes how closely a measurement approximates a true value
relative error - Accuracy has a small... Precision - describes the amount of detail in a measurement index numbers - provides a simple way to compare measurements made at different times or in different places reference value - The value at one particular time (or place) must be chosen as the... value / reference value x 100 - what is the formula to find the index number? the reference value - Ant reference value can be used to calculate an index number, but changing __________________ results in a different index number Consumer Price Index (CPI) - based on an average of prices for a sample of more than 60,000 goods, services, and housing costs. It's computed and repeated monthly The rate of Inflation - from one year to the next is usually defined as the relative change in the Consumer Price Index (CPI) True positive - a test correctly reports a positive result False positive - a test incorrectly reports a positive results
Compound interest - interest paid both on the original principal and on all interest that has been added to the original investment A= P x (1 + APR)^Y - What is the formula for Compound Interest paid once a year? A= P(1 + APR/N)^(nY) - What is the formula for Compound interest paid N times a year? APY (annual percentage yield) - is the actual percentage by which a balance increases n one year. (it equals to the APR if the interest is compounded annually. It is greater than the APR if interest is compounded more than once a year A= P x e^(APR x Y) - What is the formula for compound interest when continuously compounding? A= PMT x [(1 + APR/N)^(nY)-1] / (APR/N) - What is the formula for the Savings Plan with regular payments? annuity - An ________ is any series of equal, regular payments Ordinary annuity - An _________ is a savings plan in which payments are made at the end of each month Annuity due - An ________ is a plan in which payment are made of the beginning of each period future value -
The ____________ of an annuity is the accumulated amount at some future date present value - The ________ of a savings plan is a lump sum deposit that would give the same end result as regular payments into the plan. total return - The _________ is the percentage change in the investment value (A-P)/ P x 100% - What is the formula for total return? (A/P)^(1/Y)-1 - What is the formula for the annual return? annual return - The ________ is the annual percentage yield that would give the same overall growth stock (equity) - gives you a share of ownership in a company sell - The only way to get your money out is to ____ the stock bond - A ________ represents a promise of future cash government or corporation - You can buy a bond by paying some principal amount to the issuing... simple interest -
what is the formula for loan payments? Credit cards - differs from installment loans in that you are not required to pay off your balance in any set period of time mortgages - A home _________ is an installment loan designed specifically to finance a home. down payment - The ___________ is the amount of money you must pay up front in order to be given a mortgages or other loan. closing cost - are fees you must pay in order to be given the loan fixed rate mortgage - a ____________ is one in which the interest rate is guaranteed not to change over the life of the loan. adjustable rate mortgages - An ____________ is one where the interest rate changes based on the prevailing rates Single Married filing jointly Marred filing separately Head of household - What are the four categories of your filing states? exemptions and deduction - Both _______ and ________ are subtracted from your adjusted gross income
Exemptions - ... are fixed amount person Deductions - .... vary from one person to the next standard deduction - depends on your filing status itemized deductions - is the sum of all the individual deductions to which you are entitled progressive income tax - A __________ means that people with higher taxable income pay at a higher tax rate Marginal tax rates - are assigned to different income ranges (margins) tax credits - _________ are more valuable than tax deductions tax credit - a ___________ reduces your total tax bill by the full amount of the credit tax deductions - a ___________ reduces your taxable income by the amount of the deduction short - term capital gains - profits on items sold within 12 months of their purchase Long-term capital gains -
