## Discrete Mathematics with Applications 4th Edition

a. $\forall x$, if x is an equilateral triangle, then x is isosceles. $\forall$ equilateral triangles x, x is isosceles. b. $\forall x$, if x is a computer science student, then x needs to take data structures. $\forall$ computer science students x, x needs to take data structures.
A statement of the form $\forall x \in U$, if $P(x)$ then $Q(x)$ can always be rewritten in the form: $\forall x \in D$, $Q(x)$ by narrowing $U$ to be the domain $D$ consisting of all values of the variable $x$ that make $P(x)$ true.