# Truth Table - Symbolic Arguments - Assignment # 1 (Lecture# 1 - 10) Of MTH001 (Spring 2010)

by rafiq

Consider the following argument:

I will buy a new Honda or a used Mehran.
If I buy both a new Honda and a used Mehran, I will need a loan.
I bought a used Mehran and I do not need a loan.
Therefore, I did not buy a new Honda.

(a) Formulate the above arguments symbolically.
(b) Using the truth table determines whether or not the given argument is valid.
(c) Also mention critical row (or rows) in the truth

### Comments for Truth Table - Symbolic Arguments - Assignment # 1 (Lecture# 1 - 10) Of MTH001 (Spring 2010)

 May 11, 2010 Truth Table by: Staff Truth Table - Symbolic Arguments - Problem The problem Consider the following argument: I will buy a new Honda or a used Mehran. M OR H If I buy both a new Honda and a used Mehran, I will need a loan. (H ^ M) -->L I bought a used Mehran and I do not need a loan. M^~ (M ^ H) -->~L Therefore, I did not buy a new Honda. Therefore ~ H M = Mehran H = Honda L = Loan “OR” = a logical operation in which either or both input values produce a “true” result “AND” = (written as ^) a logical operation in which both input values must be present to produce a “true” result “NOT” = (written as ~) a negation T = True F = False The truth table will show that "If all four of our premises are true, then our conclusion must be true." The four premises are: (M OR H) must be true, M must be true, ~(M & H) must be true, and ~L must be true. Our conclusion: ~H should be true. Truth Table: The truth table will show every of possible combination of input values for buying a Honda or a Mehran, and the corresponding output value associated with those input values. Critical row: The row in which all premises are true. Truth Table M…………H…………L…………(M OR H)...M……~(M ^ H)……..~L….…….~H 1 T………… F………… F…………….T……….T…………T………….T………….T 2 T………… F………… T…………….T……….T………… T………….F………….T 3 T………… T………… F…………….T……….T………… F………….T………….F 4 T………… T………… T…………….T……….T………… F………….F………….F 5 F………… F………… F…………….F……….F………… T………….T………….T 6 F………… F………… T…………….F……….F………… T………….F………….T 7 F………… T………… F…………….T……….F………… T………….T………….F 8 F………… T………… T…………….T……….F………… T………….F………….F critical row: row 1 Thanks for writing. Staff www.solving-math-problems.com

 May 18, 2011 answer question by: Anonymous truth table for negation(pvQ)answer qestion