logic and proof

數學神童

數學神童

what is proposition,quantifiers,negations,conjunctions,disjunction,implication,equivalences?

walrein_lim88

what is proposition,quantifiers,negations,conjunctions,disjunction,implication,equivalences?
數學神童 发表于 21-1-2010 03:23 PM

1.   Proposition is a statement either true or false, cant both
2.   Quantifiers (base word is quantity) example of quantifier is ALL , SOME
3.  NEGATION(symbol is ~) mean not
4.CONJUNCTION (symbol is inverted V) mean AND
5. DISJUNCTION (symbol is V) mean OR
6.IMPLICATION(symbol one way arrow) mean IF X, then Y
7.EQUIVALENCE(symbol 2 way arrow) mean IF X, then Y and IF Y, then X

(is actually your f4 mathematical reasoning)

數學神童

are there anymore symbols?like converse and contrapositive of an implication.

walrein_lim88

are there anymore symbols?like converse and contrapositive of an implication.
數學神童 发表于 23-1-2010 01:29 AM

    No
    Converse means:
    if P then Q. converse: If Q then P
    Contrapositive is
    IF P then Q. converse: If not Q, then not P

walrein_lim88

再跟你讲多有关IMPLICATION的：
if a=0 and b=0, then ab=0  (<=is a true statement)
Converse: if ab=0, then a=0 and b=0
contrapositive, if ab not = 0, then a is not 0 and b is not 0.
Look at the both statement:
which one is true statement?
CONTRAPOSITIVE
converse sometimes maybe a false statement
but contrapositive will be always equivalent to the implication.
therefore, CONTRAPOSITIVE = IMPLICATION

DADDY_MUMMY

回复 1# 數學神童

做表出来。。。

puangenlun

(~(~p^q))^(~(p^~q))=0 ?????????????????????

walrein_lim88

(~(~p^q))^(~(p^~q))=0 ?????????????????????
puangenlun 发表于 24-1-2010 11:42 AM

    怎么等于0？？？？？？？？？？？？？？？？？

24hours

p <->q = (p - > q ) ^ ( q - > p)
               (~p v q) ^ (~q v p)

----------------------------
>de morgan
~(p v q) = ~p ^ ~q
thus:
~(p ^ ~q ) =  (~p v q )
so:
(~p v q ) = ~(p ^ ~q )
---------------------------

question continue:
~(p ^ ~q ) ^ ~(q ^ ~p)

done