These relationships are composed of sufficient conditions, necessary conditions, sufficient and necessary conditions, sufficient but not necessary conditions and necessary but not sufficient conditions.
1, sufficient condition
If the proposition "p q" is true, then P is a sufficient condition of Q, that is, if the condition P holds, the event Q will inevitably occur.
For example, "if two angles are opposite to each other, they are equal" is true, and "two angles are opposite to each other" is a sufficient condition for "two angles are equal".
In other words, if the condition that "two angles are diagonal" holds, it can be guaranteed that "two angles are equal" holds.
In short, the existence of sufficient conditions is inevitable.
2. Necessary conditions
If the proposition "p q" is true, then p is a necessary condition for q to be established.
That is to say, if the condition P is not established, the event Q will not happen.
For example, "If two angles are not equal, then these two angles must not be opposite" is true. "Two angles are equal" is a necessary condition for "two angles are diagonal".
In other words, "two corners are opposite" is necessary.
It should be noted that the necessary conditions do not guarantee the conclusion.
For example, "two angles are equal" does not guarantee that "two angles are diagonal".
In short: the necessary condition is that there is nothing wrong.