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Expert: Sherry Wallin - 4/25/2010


Question

Discrete MAth (Truth T
Q#1 Formulate the argument symbolically and test its validity using truth table. Also mention critical row.
If John studies hard then he gets A’s or he gets rich.
He doesn’t get A’s and he doesn’t get rich.
Therefore he doesn’t study hard.

Q#2 Construct circuit for Boolean expression (Mention out put at each step)
                                   (P V ~Q) ^ (P V Q)
Where, V = Vel;
      ~ = Tilde
      ^ = Hat

Answer
Mahvish~
    I can help with Q1 this way:
Let P = John studies hard;
Let Q = John gets A's;
Let R = John gets rich

If P -> Q V R
~Q ^ ~R        **Using DeMorgan's Law this is equivalent to ~(Q V R)
Therefore ~P

P ~P    Q ~Q     R  ~R   Q V R   P -> (Q V R)
_____________________________________________
T  F    T  F     T  F      T         T
F  T    T  F     T  F      T         T
T  F    F  T     T  F      T         T
F  T    F  T     T  F      F         T
T  F    T  F     F  T      T         T  
F  T    T  F     F  T      T         T
T  F    F  T     F  T      T         T
F  T    F  T     F  T      F         T

**Notice up above you really have P -> (Q V R) and ~(Q V R) so you do get ~P as your conclusion

Sorry I am not able to help you on Q2 except to say that there are 2 cases where the statement is true and 2 cases where the statement is false.

Math Prof

Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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