# NCERT Class 11-Math՚s: Chapter – 14 Mathematical Reasoning Part 9 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 5**:

Translate the following statements into symbolic form

(i) Rahul passed in Hindi and English.

(ii) and are even integers.

(iii) and are factors of .

(iv) Either or is an odd integer.

(v) A number is either divisible by or

(vi) Either or is a root of

(vii) Students can take Hindi or English as an optional paper.

**Answer**:

(i) where : Rahul passed in Hindi; q: Rahul passed in English

(ii) where is even integer; q: y is even integer

(iii) where is factor of ; is factor of ; is factor of

(iv) where is an odd integer; is an odd integer

(v) where p: a number is divisible by , it is divisibe by

(vi) where is a root of , is a root of

(vii) where *p*: student can take Hindi as an optional paper and *q*: student can take English as an optional paper.

**Question 6**:

Write down the negation of following compound statements

(i) All rational numbers are real and complex.

(ii) All real numbers are rationales or irrationals.

(iii) and are roots of the Quadratic equation

(iv) A triangle has either sides or sides

(v) is a prime number or a composite number

(vi) All prime integers are either even or odd

(vii) is equal to either or

(viii) is divisible by and

**Answer**:

(i) It is false that all rational numbers are real and complex

(ii) It is false that all real numbers are rational or irrational

(iii) is not a root of the quadratic equation or is not a root of the quadratic equation

(iv) A triangle has neither sides nor sides

(v) is not a prime number and it is not a complex number

(vi) It is false that all prime integers are either even or odd

(vii) is not equal to *x* and it not equal to

(viii) is not divisible by or it is not divisible by .

**Question 7**:

Rewrite each of the following statements in the form of conditional statements

(i) The square of an odd number is odd

(ii) You will get a sweet dish after the dinner

(iii) You will fail, if you will not study

(iv) The unit digit of an integer is or if it is divisible by

(v) The square of a prime number is not prime.

(vi) , if and are in A. P

**Answer**:

(i) If the number is odd number then its square is odd number

(ii) If you take the dinner then you will get sweet dish

(iii) If you will not study then you will fail

(iv) If an integer is divisible by then its unit digits are or

(v) If the number is prime then its square is not prime

(vi) If and are in A. P then

**Question 8**:

Form the biconditional statement , where

(i) The unit digit of an integer is zero.

It is divisible by .

(ii) A natural number is odd.

Natural number *n* is not divisible by

(iii) A triangle is an equilateral triangle.

All three sides of a triangle are equal.

**Answer**:

(i) The unit digit of an integer is zero if and only if it is divisible by 5.

(ii) A natural number *n* is odd if and only if it is not divisible by 2.

(iii) A triangle is an equilateral triangle if and only if all three sides of triangle are equal.