Without changing their meanings convert each of the followin

Without changing their meanings, convert each of the following sentences into a sentence having the form “If P, then Q.”

a) For a function to be continuous, it is sufficient that it is differentiable.

b) A function is rational if it is a polynomial

c) Whenever a surface has only one side, it is non-orientable.

d) A geometric series with ratio r converges if |r| < 1.

Solution

(a) If a function is differentiable, then it is continuous.

(b)If a function is a polynomial, then it is rational.

(c) If a surface has only one side, then it is non-orientable.

(d) If the common ratio (r) of a geometric series is such that |r| < 1, then the series is convergent.