Q.Write the negation of the following statements:

1. p: "Chennai is the capital of Tamil Nadu." $\sim p$: "Chennai is not the capital of Tamil Nadu."
2. p: "$\sqrt2$ is not a complex number." $\sim p$: "$\sqrt2$ is a complex number." (Negating a "not" statement removes the "not".)
3. p: "All triangles are not equilateral triangles" (i.e., no triangle is equilateral). $\sim p$: "There exists a triangle which is equilateral," i.e., "Some triangles are equilateral triangles."
4. p: "The number 2 is greater than 7." $\sim p$: "The number 2 is not greater than 7."
5. p: "Every natural number is an integer." $\sim p$: "There exists a natural number which is not an integer."
   ✓Final answer

   (i) Chennai is not the capital of Tamil Nadu. (ii) $\sqrt2$ is a complex number. (iii) Some triangles are equilateral triangles. (iv) 2 is not greater than 7. (v) There exists a natural number which is not an integer.

Insert or remove "not" at the appropriate place. For a universal claim ("all"/"every"), the negation becomes an existential claim ("there exists ... not"); for a statement that already contains "not", negating it removes the "not".

• Double-negating or under-negating a sentence that already contains "not" (part ii).
• Negating "all triangles are not equilateral" as "all triangles are equilateral" instead of the correct existential form "some triangle is equilateral".