Appendix 1 · Proofs in Mathematics

NCERT Class 10 Maths Exercise A1.4

All 2 questions of NCERT Class 10 Maths Exercise A1.4 (Proofs in Mathematics), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   State ​the ​negations for the following statements:

   1. (i)Man is mortal.
   2. (ii)​Line $l$ is parallel to line $m$.
   3. (iii)This chapter has many exercises.
   4. (iv)All integers are rational numbers.
   5. (v)​Some prime numbers are odd.
   6. (vi)No student is lazy.
   7. (vii)Some cats are not black.
   8. (viii)There is ​no real number $x$, such that $\sqrt{x}=-1$.
   9. (ix)2 divides the positive integer $a$.
   10. (x)​Integers $a$ ​and $b$ are coprime.
   Show answer

   (i) Man is not mortal. (ii) Line $l$ is not parallel to line $m$. (iii) The chapter does not have many exercises. (iv) Not all integers are rational numbers. (v) All prime numbers are not odd. (vi) Some students are lazy. (vii) All cats are black. (viii) There is at least one real number $x$ such that $\sqrt{x}=-1$. (ix) 2 does not divide the positive integer $a$. (x) Integers $a$ and $b$ are not coprime.

   Step-by-step solution →
2. Q2
   In each of the following questions, there are two statements. State if the second is ​the negation of the first ​or not.

   1. (i)Mumtaz is ​hungry. / Mumtaz is ​not hungry.
   2. (ii)Some cats are black. / Some cats are brown.
   3. (iii)All elephants are huge. / One elephant ​is not huge.
   4. (iv)All fire engines are red. / All ​fire engines are not red. ​
   5. (v)No man ​is a cow. / Some men are cows.
   Show answer

   (i) Yes (ii) No (iii) No (iv) No (v) Yes

   Step-by-step solution →