## ajprincess 3 years ago prove\[(\neg p\wedge(\neg q\wedge r))\vee(q\wedge r)\vee(p\wedge q)=r\]

1. ajprincess

|dw:1338094648240:dw| prove this using laws of algebra of propositions.

2. ajprincess

@amistre64, @jamesJ, @turingtest

3. ajprincess

plzzz help me.

4. ajprincess

|dw:1338095286775:dw| Except this other all are right.

5. ajprincess

ya sure. thanx. :) can u help me to prove it if u dnt mind.

6. TuringTest

not used to this kind of thing,; I'm not sure what the technically right approach would be start making assumptions I guess...

7. ajprincess

ha k. thanx. @jamesJ if u dnt can u plzzz help me with this question?

8. ajprincess

*mind

9. JamesJ

How have you proved these sorts of things in the past? The most straight-forward way to show this would be write out a truth table with eight rows, one row for each of the truth value combinations of p, q and r

10. ajprincess

i am ok with proving it using truth table. this is one of my past paper question. they hav askd to prove t using laws of algebra of propositions. bt I am nt ued to it.

11. ajprincess

@asnaseer can u plzz help me vth this if u dnt mind.

12. ajprincess

@JamesJ u too. can u help me plzzz

13. JamesJ

So you want to prove this now using propositions?

14. ajprincess

ya.

15. ajprincess

I tried bt was unable to get t.

16. JamesJ

I just constructed the truth table and the question as written here looks wrong. Could you please triple check it.

17. ajprincess

ha k.

18. JamesJ

I think it might be this, but you check it! \[ (\neg p\wedge(\neg q\wedge r))\vee(q\wedge r)\vee(p\wedge r)=r \]

19. ajprincess

ya that's it. sooo sorrry for the mistake.

20. JamesJ

ok, well you factor out ^ r from each of these terms and you have ( ~p^~q) v q v p ) ^ r

21. JamesJ

and ( ~p^~q) v q v p is always true. Hence the entire expression is equivalent to TRUE ^ r = r

22. ajprincess

bt hw do v knw that ( ~p^~q) v q v p is always true?

23. JamesJ

because ~p^~q = ~(p v q) and hence (~p^~q) v q v p = ~(p v q) v (p v q)

24. JamesJ

...and X v ~X is always true.

25. ajprincess

I get t nw. thanxxxxxxxx a lot.