Consider the following three statements:
(A) If $$3 + 3 = 7$$ then $$4 + 3 = 8$$
(B) If $$5 + 3 = 8$$ then earth is flat.
(C) If both (A) and (B) are true then $$5 + 6 = 17$$.
Then, which of the following statements is correct?

We evaluate the truth value of each statement using the rule that a conditional $$p \Rightarrow q$$ is false only when $$p$$ is true and $$q$$ is false.

Statement (A): "If $$3 + 3 = 7$$ then $$4 + 3 = 8$$." The hypothesis $$3 + 3 = 7$$ is false. A conditional with a false hypothesis is vacuously true. So (A) is true.

Statement (B): "If $$5 + 3 = 8$$ then the earth is flat." Here $$5 + 3 = 8$$ is true, but "the earth is flat" is false. A conditional with a true hypothesis and false conclusion is false. So (B) is false.

Statement (C): "If both (A) and (B) are true then $$5 + 6 = 17$$." Since (B) is false, the hypothesis "(A) and (B) are true" is false. Therefore (C) is vacuously true. So (C) is true.

Thus (A) and (C) are true while (B) is false.