Translate prose with quantified statements to symbolic and find the negation of quantified statements.
Negate the statement and simplify so that no quantifier or connective lies within the scope of a negation:
(∀x)(∃y)(P(x,y)→Q(x,y))
(b.) Consider the domain of people working at field site HuppaLoo. Let M(x,y): x has access to mailbox y.
Translate into predicate logic using quantifiers:
Every worker at Huppaloo has access to some mailbox.
There exists a worker at Huppaloo who has access to all mailboxes.
(c.) Consider the domain of real numbers. Compare the following two statements and explain their meaning (in words).
(∀x)(∃y)(x+y=1)
(∃y)(∀x)(x+y=1)