Negations

Key Notes:

What is Negation?

  • Negation means expressing the opposite of a statement.
  • It turns an affirmative (positive) statement into a negative one.

Common Negation Words

Not, no, never, none, nothing, nobody, nowhere, neither, nor

Prefixes like un-, in-, im-, dis-, non- also indicate negation.

  • Examples: unhappy, impossible, disagree, inactive

Negating Sentences

Insert “not” after the helping verb:

  • She is singing. → She is not singing.
  • They have finished. → They have not finished.
  • If no helping verb is present, use “do/does/did” + not:
  • He eats apples. → He does not eat apples.

Double Negatives (Avoid These!)

Using two negatives in one sentence makes it grammatically incorrect in standard English.

  • ❌ I don’t need no help.
  • ✅ I don’t need any help.

Negation in Questions

To ask a negative question:

  • Didn’t you go to the party?
  • Isn’t she your friend?

Negation in Logic (Mathematical/Philosophical Contexts)

In logical reasoning, negation means the opposite of a proposition.

  • If P = “It is raining”, then ¬P = “It is not raining.”

Changing Affirmative to Negative (Without Changing Meaning)

Example:

  • Affirmative: Everyone was present.
  • Negative: No one was absent.

✍️ Examples of Negation

AffirmativeNegative
She is happy.She is not happy.
They went home.They did not go home.
I know the answer.I do not know the answer.
Everyone agreed.No one disagreed.

Learn with an example

🎯 What is the negation of the following inequality?–k≥–10

  • k < 10
  • k ≥ 10
  • –k > –10
  • –k < –10
  • The given inequality is –k≥–10, which means –k is greater than or equal to –10.
  • The negation of that inequality is –k is not greater than or equal to –10. That is equivalent to –k is less than –10, which can be written as –k<–10.
  • So, the negation of –k≥–10 is –k<–10.

🎯 What is the negation of the following inequality?u≤5

  • u > 5
  • u ≥ 5
  • –u ≤ –5
  • –u > –5
  • The given inequality is u≤5, which means u is less than or equal to 5.
  • The negation of that inequality is u is not less than or equal to 5. That is equivalent to u is greater than 5, which can be written as u>5.
  • So, the negation of u≤5 is u>5.

🎯 What is the negation of the following inequality?–q≥–10

  • –q ≤ –10
  • –q > –10
  • –q < –10
  • q ≥ 10
  • The given inequality is –q≥–10, which means –q is greater than or equal to –10.
  • The negation of that inequality is –q is not greater than or equal to –10. That is equivalent to –q is less than –10, which can be written as –q<–10.
  • So, the negation of –q≥–10 is –q<–10.

Let’s practice!🖊️