Questions: Being a month is a for being January. necessary sufficient

Solution Steps

To determine if being a month is necessary or sufficient for being January, we need to understand the logical relationship between the two statements. Specifically, we need to check if being January implies being a month and if being a month implies being January.

To analyze the relationship between being a month and being January, we denote:

• Let \( A \) represent "being January."
• Let \( B \) represent "being a month."

We need to evaluate the implications:

1. \( A \implies B \) (If it is January, then it is a month.)
2. \( B \implies A \) (If it is a month, then it is January.)

From our analysis:

• The statement \( A \implies B \) is true because January is indeed a month.
• The statement \( B \implies A \) is false because there are other months besides January.

Since \( A \implies B \) is true and \( B \implies A \) is false, we conclude that being a month is necessary for being January, but not sufficient. Thus, we can express this as:

• Being a month is necessary for being January.

Final Answer