Example on Rules of Inference

Show that the premises

“If you send me an e-mail message, then I will finish writing the
program,”

“If you do not send me an e-mail message, then I will go to sleep early,” and

“If I go to sleep early, then I will wake up feeling refreshed”

lead to the conclusion

“If I do not finish writing the program, then I will wake up feeling refreshed.”

Answer

Things you need to know

Refer short notes : http://www.techtud.com/short-notes/rules-inference

Now,  Let

p : “You send me an e-mail message”

q:  “I will finish writing the program”

r:  “I will go to sleep early”

s: “I will wake up feeling refreshed”

 

Then the premises are p → q, ¬p → r, and r → s.

The desired conclusion is ¬q → s

 

Step Reason
1. p → q Premise
2. ¬q → ¬p Contrapositive of (1)
3. ¬p → r Premise
4. ¬q → r Hypothetical syllogism using (2) and (3)
  5. r → s Premise
6. ¬q → s Hypothetical syllogism using (4) and (5)

 

 

 

 

 

1Comment
aditya @adityakumar100
24 Aug 2017 12:46 pm

Really good post ..thankyou