Questions: Translate the argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. You got an A in Math, or I am happy. Today I'm happy. Therefore, Today you did not get an A in Math. (i) Click the icon to view tables of standard valid and invalid forms of arguments. Let p represent "Today you got an A in Math," and let q represent "Today I'm happy." Select the correct choice below and fill in the answer box with the symbolic form of the argument. (Type the terms of your expression in the same order as they appear in the original expression.) A. The argument is invalid. In symbolic form the argument is B. The argument is valid. In symbolic form the argument is

Translate the argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. You got an A in Math, or I am happy. Today I'm happy. Therefore, Today you did not get an A in Math. (i) Click the icon to view tables of standard valid and invalid forms of arguments. Let p represent "Today you got an A in Math," and let q represent "Today I'm happy." Select the correct choice below and fill in the answer box with the symbolic form of the argument. (Type the terms of your expression in the same order as they appear in the original expression.) A. The argument is invalid. In symbolic form the argument is B. The argument is valid. In symbolic form the argument is
Transcript text: Translate the argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. You got an A in Math, or I am happy. Today I'm happy. $\therefore$ Today you did not get an A in Math. (i) Click the icon to view tables of standard valid and invalid forms of arguments. Let p represent "Today you got an A in Math," and let q represent "Today I'm happy." Select the correct choice below and fill in the answer box with the symbolic form of the argument. (Type the terms of your expression in the same order as they appear in the original expression.) A. The argument is invalid. In symbolic form the argument is $\square$ B. The argument is valid. In symbolic form the argument is $\square$
failed

Solution

failed
failed

Solution Steps

To solve this problem, we need to translate the given statements into symbolic form using the provided variables \( p \) and \( q \). Then, we will determine the validity of the argument by comparing it to standard forms or using a truth table.

  1. Translate the statements into symbolic form:

    • "You got an A in Math, or I am happy" translates to \( p \lor q \).
    • "Today I'm happy" translates to \( q \).
    • "Today you did not get an A in Math" translates to \( \neg p \).

  2. Combine these statements into an argument:

    • Premises: \( p \lor q \) and \( q \)
    • Conclusion: \( \neg p \)

  3. Determine the validity of the argument by constructing a truth table or comparing it to standard forms.

Step 1: Translate Statements into Symbolic Form

We define the following:

  • Let \( p \) represent "Today you got an A in Math."
  • Let \( q \) represent "Today I'm happy."

The statements can be translated as follows:

  • "You got an A in Math, or I am happy" translates to \( p \lor q \).
  • "Today I'm happy" translates to \( q \).
  • "Today you did not get an A in Math" translates to \( \neg p \).
Step 2: Formulate the Argument

The argument can be structured as:

  • Premises:
    1. \( p \lor q \)
    2. \( q \)
  • Conclusion: \( \neg p \)
Step 3: Determine Validity of the Argument

To assess the validity, we analyze the premises and conclusion:

  • The argument is valid if the conjunction of the premises and the negation of the conclusion is unsatisfiable: \[ (p \lor q) \land q \land \neg p \]

Upon evaluation, we find that this expression is satisfiable, indicating that there are scenarios where the premises hold true while the conclusion does not.

Final Answer

The argument is invalid. In symbolic form, the argument is \( (p \lor q), q \vdash \neg p \).

Thus, the answer is \( \boxed{A} \).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 7% margin of error at a 90% confidence level, what size of sample is needed? Give your answer in whole people.
failedAnswered
Given the following compound C8H10N4O2 Answer the following: Given the moles of Hydrogen (H) which of the following is the conversion factor to calculate the moles of C8H10N4O2 ? [Select] 1) 1 mol H / 10 mol C8H10N4O2 2) 10 mol H / 1 mol C8H10N4O2 4) 1 mol C8H10N4O2 / 10 mol H Given the moles of C8H10N4O2 which of the following is the conversion factor to calculate the moles of carbon (C)? [Select] 1) 1 mol C / 8 mol C8H10N4O2 2) 8 mol C / 1 mol C8H10N4O2 3) 8 mol C8H10N4O2 / 1 mol C 4) 1 mol C8H10N4O2 / 8 mol H
failedAnswered
Decide whether the relation is a function. x -1 2 6 9 10 y 8 -4 1 8 9 Select one: a. Not a function b. Function
failedAnswered
Un automóvil realiza un recorrido en línea recta, primero recorre 28.94 km hacia un sentido y después realiza 12.01 km sobre la misma línea, pero en sentido contrario. Todo el recorrido lo hace en un cuarto de hora ¿Cuál es la magnitud de la velocidad ( km / h ) del automóvil? Únicamente coloca el valor numérico, SIN UNIDADES. Utiliza al menos 4 DECIMALES para el procedimiento. Coloca únicamente 2 DECIMALES en el resultado sin redondear.
failedAnswered
Rita takes out a loan for her college tuition from a bank that charges simple interest at an annual rate of 5%, her loan is for 7700 for 4 months. Assume each month is 1/12 of a year. Answer each part below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Find the interest that will be owed after 4 months. (b) Assuming Rita doesn't make any payments, find the amount owed after 4 months.