Originally Posted by
Noxide Is the inverse of the following compound statement correct?
Statement:
(For all fruit x, x is red) => [ (all houses are blue) or (some chickens are white) ]
Inverse:
(For some fruit x, x is not red) => [ (some houses are not blue) and (no chickens are not white) ]
My confusion comes from the hypothesis of the implication. It is of the form
[ (universal quantifier)(subject), (subject)(verb)(predicate) ]. I know a statement must be of the form [ (subject)(verb)(predicate) ] and also that the negation of [ (universal quantifier)(statement) ] is [ (existential quantifier)(negation of statement) ] but what is the negation of [ (universal quantifier)(subject), (subject)(verb)(predicate) ]?