Discrete Math question

[Kcashew]

I apologize if this may be out of the ordinary, but I didn't see anywhere else to post questions about discrete mathematics.

I had tried to employ the 12th logical equivalence for this type of problem, but I am unsure of how to proceed from here.

Did I make a mistake somewhere?

If so, how may I correct it?

 

[pka]

\(\left[ {(p \to q) \vee (q \to r)} \right] \wedge (r \to s)\): The instructions are to simplify.
I must say that having first taught this material in the fall of 1964 I still find this a meaningless question.
I sure that whoever wrote the question will heartily disagree because to her/him it is clear what is required.
AND that is find. I just don't see it.

 

[Steven G]

You showed us your answer can we please see your work? You want us to tell you where you made a mistake but failed to show us your work. That will be hard for us to do. Did you draw a truth table for the given problem and your results? Did the truth table verify your results?

 

[Dr.Peterson]

I apologize if this may be out of the ordinary, but I didn't see anywhere else to post questions about discrete mathematics.

I had tried to employ the 12th logical equivalence for this type of problem, but I am unsure of how to proceed from here.

Did I make a mistake somewhere?

If so, how may I correct it?

This is the right place to put the question, and you have shown one step of your work, which is correct.

The trouble is, it isn't at all clear what the goal is; what is considered "simple"? Have you been told what form is preferred? Do you have any examples of similar problems with their answers?

 

[pka]

Look at the truth table for \(\left[ {(p \to q) \vee (q \to r)} \right] \wedge (r \to s)\).
That indicates there is little simplification. Lets distribute the conjunction over the disjunction.
\(\left[ {(p \to q)\wedge (r \to s)] \vee [(q \to r)}\wedge (r \to s) \right]\)
Now using hypothetical syllogism we can reduce it to:
\(\left[ {(p \to q)\wedge (r \to s)] \vee [(q \to s)} \right]\)
I do not consider that to be a simplification. If an answer were given I would like to see it

 

[topsquark]

I apologize if this may be out of the ordinary, but I didn't see anywhere else to post questions about discrete mathematics.

I had tried to employ the 12th logical equivalence for this type of problem, but I am unsure of how to proceed from here.

Did I make a mistake somewhere?

If so, how may I correct it?

And please when you post another image try to make it less sloppy.

-Dan