Modeling and manipulating formal logic:

(a) Evaluate (simplify) this negation: x D, y E | P(x, y)

(b) Write the following propositions symbolically. If there is ambiguity, write all possible interpretations. Don't worry whether it is true or false. Then negate the expression, simplify, and express the negation in English.

i. All shoes are on sale

ii. Every stop sign is red

iii. There is a whole number greater than all others.

iv. Any natural number can be divided by 4 (natural numbers being numbers we count with 1,2,3)