Necessary and sufficient conditions in theorems

When students and professional mathematicians are asked what the difference between necessary and sufficient conditions is, they often have difficulty answering the question. Even when presented with concrete formulations of state and asked what the difference between necessary and sufficient conditions means, the answer is not always correct. Meanwhile, these two notions are widespread in modern mathematics. This article attempts to consider necessary and sufficient conditions, hoping to increase the mathematical culture of both readers and their authors.