A student makes the following argument. if I receive a good grade, the instructor teaches well. I didn't receive a good grade. Therefore, the instructor didn't teach well. is the student's argument valid? Let A be the statement, "I receive a good grade" and B be the statement, " the instructor teaches well." Then, rewrite the above paragraph using A and B.
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A: Question:
A student makes the following argument.
if I receive a good grade, the instructor teaches well. I didn't receive a good grade. Therefore, the instructor didn't teach well.
is the student's argument valid? Let A be the statement, "I receive a good grade" and B be the statement, " the instructor teaches well." Then, rewrite the above paragraph using A and B.
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- When you use a mortgage to purchase a home, the lending institution effectively owns the home. You buy back part ownership in the home with each monthly payment. The part you have bought back is your equity in the home. If the mortgage amount is P dollars, the monthly interest rate is r as a decimal, and the term of the mortgage is t months, then your equity after k payments is E(k) = P((1 + r)k − 1) (1 + r)t − 1 dollars. In this exercise, assume that the mortgage amount is $200,000, the APR is 6% so r = .06/12 and the term of the loan is 30 years (360 months). (a) Find a formula for the equity. (b) Make a graph of the equity over 360 months, the term of the loan. (c) Does the graph show that you have half-ownership in the home halfway through the term of the mortgage? Halfway through the term of the mortgage corresponds to k1 = _______ payments. From the graph, we see that E(k1) is ________ half of the mortgage amount, so we _______ have half-ownership in the home…When you borrow money to buy a house, a car, or for some other purpose, you repay the loan by making periodic payments over a certain period of time. Of course, the lending company will charge interest on the loan. Every periodic payment consists of the interest on the loan and the payment toward the principal amount. To be specific, suppose that you borrow $1,000 at an interest rate of 7.2% per year and the payments are monthly. Suppose that your monthly payment is $25. Now, the interest is 7.2% per year and the payments are monthly, so the interest rate per month is 7.2/12 = 0.6%. The first months interest on $1,000 is 1000 0.006 = 6. Because the payment is $25 and the interest for the first month is $6, the payment toward the principal amount is 25 6 = 19. This means after making the first payment, the loan amount is 1,000 19 = 981. For the second payment, the interest is calculated on $981. So the interest for the second month is 981 0.006 = 5.886, that is, approximately $5.89. This implies that the payment toward the principal is 25 5.89 = 19.11 and the remaining balance after the second payment is 981 19.11 = 961.89. This process is repeated until the loan is paid. Write a program that accepts as input the loan amount, the interest rate per year, and the monthly payment. (Enter the interest rate as a percentage. For example, if the interest rate is 7.2% per year, then enter 7.2.) The program then outputs the number of months it would take to repay the loan. (Note that if the monthly payment is less than the first months interest, then after each payment, the loan amount will increase. In this case, the program must warn the borrower that the monthly payment is too low, and with this monthly payment, the loan amount could not be repaid.)Write the following compound statement in terms of the simple statements p, q, and r. "I go to office hours and ask questions, and my professor does not remember me." p: I go to office hours. q: I ask questions. r: My professor remembers me.
- When you borrow money to buy a house, a car, or for some other purposes, then you typically repay it by making periodic payments. Suppose that the loan amount is L, r is the interest rate per year, m is the number of payments in a year, and the loan is for t years. Suppose that i = (r / m) and r is in decimal. Then the periodic payment is: You can also calculate the unpaid loan balance after making certain payments. For example, the unpaid balance after making k payments is: where R is the periodic payment. (Note that if the payments are monthly, then m = 12.) Instructions Write a program that prompts the user to input the values of L, r, m, t, and k. The program then outputs the appropriate values. Your program must contain at least two functions, with appropriate parameters, to calculate the periodic payments and the unpaid balance after certain payments. Make the program menu driven and use a loop so that the user can repeat the program for different values. Example of…Given a nonterminal A, which of the following statements is true about FIRST(A) and FOLLOW(A)? a.FIRST(A) can be a nonterminal b.FOLLOW(A) cannot be $ c.FOLLOW(A) can be ε d.FIRST(A) can be εWrite the inverse of the following statement: “If it is winter, then it is snowing.” ____________________________________________________________________
- Determine the truth value of the statement (~p ∨ q) ∨ (r ∧ q) using the following conditions. a) p is false, q is true, and r is true. b) p is true, q is false, and r is false. a) If p is false, q is true, and r is true, what is the value of (~p ∨ q) ∨ (r ∧ q)? True? False? b) If p istrue, q is false, and r is false, what is the value of (~p ∨ q) ∨ (r ∧ q)? True? False?Is the following argument valid? Prove your answer by replacing each proposition with a variable to obtain the form of the argument. Then prove that the form is either valid or invalid. He studied for the test or he failed the test or both.He passed the test.∴ He studied for the test.For the following statement, write down a logically equivalent statement which containsno operators other than ¬ and ∨: P ∧ (Q → R)
- Write the statement in words if: p: Firemen work hard. q: Firemen wear red suspenders 3) ~p → q10. Let p be the statement “He gets frustrated.” and q be the statement “He will be able to complete the job.” Translate ~(p ∧ q) into the equivalent statement.(De Morgan’s Laws) In this chapter, we discussed the logical operators &&, ||, and !. DeMorgan’s Laws can sometimes make it more convenient for us to express a logical expression. Theselaws state that the expression !(condition1 && condition2) is logically equivalent to the expression(!condition1 || !condition2). Also, the expression !(condition1 || condition2) is logically equivalentto the expression (!condition1 && !condition2). Use De Morgan’s Laws to write equivalent expressions for each of the following, and then write a program to show that both the original expressionand the new expression in each case are equivalent.a) !(x < 5) && !(y >= 7)b) !(a == b) || !(g != 5)c) !((x <= 8) && (y > 4))d) !((i > 4) || (j <= 6))