Write the following argument in “standard form.” Make sure to identify the concl

Question

Write the following argument in “standard form.” Make sure

to identify the conclusion. Before using any symbolic techniques, evaluate

whether you believe the argument to be valid or not. Then translate the

argument into the language of sentential logic. Be sure to indicate what

each sentential variable represents.

Argument:

Either Sharanya won’t go to the concert or she will miss a stu-

dent loan payment. For when Sharanya’s hours at her job are reduced, either

she cuts spendings or she incurs debts. If she cuts spendings, then Sharanya

won’t go to the concert. Unless Sharanya’s parents help her financially or

she wins the lottery, she will miss a student loan payment if she incurs debts.

And neither will it be the case that Sharanya’s parents help her financially

nor will it happen that she wins the lottery.

Explanation / Answer

Below are the steps to write the argument in “standard form. P1, P2... are Premises and C1, C2,.. are conclusions.

P1. Either Sharanya won’t go to the concert or she will miss a student loan payment.

P2. For when Sharanya’s hours at her job are reduced, either she cuts spendings or she incurs debts.

P3. If she cuts spendings, then Sharanya won’t go to the concert.

P4. Unless Sharanya’s parents help her financially or she wins the lottery, she will miss a student loan payment if she incurs debts.

P5. Neither will it be the case that Sharanya’s parents help her financially nor will it happen that she wins the lottery.

C1 Therefore, from P4 and P5,  If Sharanya incurs debts,she will miss a student loan payment

P2. For when Sharanya’s hours at her job are reduced, either she cuts spendings or she incurs debts.

P3. If she cuts spendings, then Sharanya won’t go to the concert.

C1 If Sharanya incurs debts, she will miss a student loan payment

C2 Therefore, from P2 and P3 and C1, For when Sharanya’s hours at her job are reduced, either Sharanya won’t go to the concert or she will miss a student loan payment.

P1. Either Sharanya won’t go to the concert or she will miss a student loan payment.

C2 For when Sharanya’s hours at her job are reduced, either Sharanya won’t go to the concert or she will miss a student loan payment.

C3 Sharanya’s hours at her job are reduced

So, final conclusion is Sharanya’s hours at her job are reduced

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