Rules of inference
Rules of inference:
Rules of inference for quantified statements:
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Submitted by virtualgate on 8 May, 2017 - 12:06
Rules of Inference
Edited:
- Virtual GATE @virtualgate added a2 Mar 2017
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.”
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) |