Interesting to see people who can't negate B properly go for "too strong" in their analysis. Some
golden rules for negation I learnt from this question to carry forward.
Type-1: When you have quantifiers + verb -> Always negate the quantifier and leave the verb alone
Original: "
All guests
ate the cake."
✅ Correct Negation: "
Not all guests
ate the cake." (or "Some guests did not eat the cake.") Because Not all As are Bs is logically equivalent to Some As are not Bs.
❌ Common Mistake: "
All guests
did not eat the cake." (This is incorrect because it means no one ate the cake, which is a different statement.)
The same principle applies for all the quantifiers: No, none, anyone, some, few, many etc.
The same principle applies when the verb is paired with modal verbs: must, shall, will, should, would, can, could, may, and might etc
Another example is "
Any guest
can eat the cake"
✅ Correct Negation: "
Not all guests
can eat the cake" (or "Some guests cannot eat the cake")
Type-2: Options with Independent clauses. Ex: Sentences with because -> throw because/since etc out of the window
Original: "The game was cancelled because it was raining."
✅ Correct Negation: "The game was not cancelled."
❌ Incorrect Negation: "The game was cancelled because it was not raining."
Type-3: Conditional statements: If A ->B, then show If A, then B may not happen
Original: "If a product is high quality, then it will sell well.".
✅ Correct Negation: "A product can be high quality, and yet not sell well." (ie Just show If A, then B can happen)
❌ Incorrect Multiple Negation: "If a product is not high quality, then it will not sell well." (Shouldn't negate both A and B)
Type-3: Compound statements:-> A and B -> Not both (A and B)
Original Statement: "An applicant must speak French
and English"
✅ Correct Negation: "An applicant may not need both of those languages."
❌ Incorrect Negation: "An applicant must not speak French and English"
Now try this,
If a server fails its security audit, then
all administrators on that server
must reset their passwords
and enable two-factor authentication.
✅ Correct Negations:
"A server can fail its security audit, and yet not all administrators on that server must reset their passwords and enable two-factor authentication"
"A server can fail its security audit, and yet some administrator on that server does not have to reset both their password and enable two-factor authentication."