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Ask for advice: [Mathematical Logic] What is the negative proposition that "efforts may not necessarily succeed"?
You must first understand that only conditional propositions have so-called negative propositions.

1: efforts may not necessarily succeed.

It is a conditional proposition, and it will be successfully denied. Namely:

②: No, efforts will surely succeed;

Judging from the final result (such as truth table), the negation of conditional proposition is no longer a real conditional proposition. Therefore, even if you ask for its negative proposition, it should be carried out under the negative word-only under the negative word, it still retains the "shape" of the conditional proposition. Then (2) the negative proposition is:

3: No, if you don't succeed, you must have no effort;

Change it, that is:

4. Unsuccessful, not necessarily without efforts;

I said that "the negation of conditional proposition is no longer a real conditional proposition", that is to say, this proposition is more suitable to be expressed by joint proposition; In addition, the modal particle "must" is used in your question, which can be expressed by quantifiers:

① = ② = ③ = ④ = Some people (or sometimes): tried and failed;

If the result you give is not necessarily successful, then don't work hard. Regardless of right or wrong. First of all, this is ambiguous:

(1) Not necessarily: (if) you succeed (if) you don't work hard;

Success doesn't necessarily mean no effort.

= Some people (or sometimes): success, hard work;

(2) (if) you may not succeed, (just) don't work hard;

= (If) some people (or sometimes) are unsuccessful, (then) all people (at any time) don't work hard;

It can be seen that they are not the same as your original ideas in meaning. So this result is definitely wrong.