- Precedence of logical operators is as follows:

**¬ > ∧ > ∨ > → > ↔**

where, **¬ , ∧ , ∨ **is left associative** **and** → , ↔ **is right associative.

Example: P** →**Q →R can be wriiten as (P** →(**Q →R))
- Following are the rules of inference:

- Modus Ponens:

P

P**→**Q

________

Q

________
- Modus Tollens:

¬Q

P->Q

________

¬P

________
- Disjunctive Syllolgism:

P∨Q

¬P

________

Q

________
- Constructive Dilemma:

(P**→**Q ) ∧ (R**→**S )

(P∨R )

________

Q∨S

________
- Destructive Dilemma:

(P**→**Q ) ∧ (R**→**S )

(¬Q∨¬S)

________

¬P∨¬R

________
- Disjunctive Syllolgism:

P∨Q

¬P

________

Q

________

Example:

If child studies , mom will not scould

Mom scoulded

Inference: Child did not study.

Ans. p = child studies

q = Mom scould

p->~q

q

_____

~p ///using Modus Tollens

_____

~p means child did not study.

Thus , given inference is true.

@shivani

pls explain point 3 .what are the condition for checking hamilton path

start from a vertex and you can trace each vertex exactly once without repeating vertices but you cant reach to the starting vertex without repeating try it.

One more point that can be added is this graph contains K5 and its isomorphic image as well..