9. Given: a = b
azo
Prove: b c
The indirect proof is
a. Suppose b = c. Then a = c by the transitive property. But we
know that a + c. This statement is a contradiction. Therefore,
our supposed relationship is false, and its negation is true.
b. Suppose a = c. Then b = c. But we know that a = b and not
a + c. Therefore, b #c.
c. Suppose a > 25, such as a = 26. Then 2(26) < 51 or 52 < 51.
This is a contradiction, so a > 25 is false and a < 25 is true.
d. Suppose a = 2. Then (2)? + 2 = 8, which means 6 = 8. This
is a contradiction because 8 = 8. Therefore, a = 2 is false and
a + 2 is true.