A conditional statement is an if-then statement that consist of an hypothesis and a conclusion. In formal logic the hypothesis is denoted with the letter p and the conclusion with the letter q; they are joint by the logical ⇒. We read the conditional statement p⇒q as if p then q. A conditional is statement is true if the conclusion is true, and is only false if the hypothesis is true but the conclusion is false.
Now let's analyze each one of your examples:
A. If next month is January, then this month is the last of the year.
Hypothesis: This month is the last of the year.
Conclusion: Next month is January.
The last month of the year is December, and January follows December. so this is a true conditional statement, but neither the hypothesis nor the conclusion were correctly identified.
The correct ones are:
Hypothesis: Next month is January.
Conclusion: This month is the last of the year.
B. Next month is February, so this month is the last month of the year.
This is not even a conditional statement. The first sentence "Next month is February" is just stating a fact; it not a hypothesis.
C. Next month is February, so this month is the last month of the year.
This is the same example as before, and just like before it is not even a conditional statement.
D. None of above
Since the hypothesis and conclusion of A are wrong, and B and C are not even conditional statement, D is the correct answer.
