Answer
a. $\forall$ nonzero fractions x, the reciprocal of x is a fraction.
$\forall x$ , if x is a nonzero fraction, then the reciprocal of x is a fraction.
b. $\forall$ polynomial functions x, the derivative of x is a polynomial function.
$\forall x$, if x is a polynomial function, then the derivative of x is a polynomial function.
c. $\forall$ triangles x, the sum of the angles of x is 180 degrees.
$\forall x$ , if x is a triangle, then the sum of the angles of x is
180 degrees.
d. $\forall$ irrational numbers x, the negative of x is irrational.
$\forall$ x, if x is irrational, then the negative of x is irrational.
e. $\forall$ even integers x and y, the sum of x and y is even.
$\forall$ x and y, if x and y are even integers, then the sum of x
and y is even.
f. $\forall$ fractions x and y, the product of x and y is a fraction.
$\forall$ x and y, if x and y are fractions, then the product of x and y is a fraction.
Work Step by Step
A statement of the form ∀x∈U, if P(x) then Q(x)
can always be rewritten in the form:
∀x∈D, Q(x)
by narrowing U to be the domain D consisting of all values of the variable x that make P(x) true.
