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)