If a + 1 = b, then b > a.

Question

Consider the following conditional statement.

If a + 1 = b, then b > a.

A. Create a pair of values for a and b in which the numerical relationship shown in the given conditional statement is true. In your final answer, include the values of the variables and proof of truth.

B. Is it possible to create a pair of values for a and b in which the numerical relationship shown in the given conditional statement is false? Use complete sentences to explain your answer.

Answer 1

Here is a direct proof:

if a+1 = b, then a = b-1, with b>b-1 for ANY real number B.

THen b> b-1=a, so b>a.

Here is a proof by contradiction:

Suppose a+1=b and B<a

then b+1 < a+1 <-- adds 1 to both sides

b+1 < b <-- substitutes a+1=b

1<0 contradiciton.

THerefore B>a MUST follow and hold true