Answer
a. False. There is no object that has a different color from every other object.
b. Formal version: ∃y(∀x(x = y → ∼SameColor(x, y)))
c. Formal negation: ∀y(∃x(x = y ∧ SameColor(x, y)))
Work Step by Step
c. ~(∃y(∀x(x = y → ∼SameColor(x, y))))
$\equiv$ $\forall$y ~(∀x(x = y → ∼SameColor(x, y)))
(by the law of negating a $\exists$ statement)
$\equiv$ $\forall$y ($\exists$x ~(x = y → ∼SameColor(x, y)))
(by the law of negating a $\forall$ statement)
$\equiv$ $\forall$y ($\exists$x (x = y $\land$ SameColor(x, y)))
(by the law of negating an if-then statement)
