I came across following problem
"Every intelligent student is not honest."
And I have to convert this in quantifiers. Straight conversion will be:
∀x [(S(x)∧I(x)) → ¬H(x)] ...(i)
However the solution is given in existential quantifier as follows:
∃x [S(x)∧I(x)∧¬H(x)] ...(ii)
with explanation "There exist intelligent students who are not honest"
Though this sounds and looks correct, how can I convert (i) to (ii) mathematically I mean without verbal interpretation, may be by double negation?