Class 11 Maths Ncert Solutions Chapter 14 Ex 14.3 Mathematical Reasoning PDF

Class 11 Maths Ncert Solutions Ex 14.3

Class 11 Maths Ncert Solutions Chapter 14 Ex 14.3

 Q.1:

(i). Every real number is not complex number and every rational number is a real number.

(ii).  Square of any integer is negative or positive.

(iii).  The sand easily heats up due to the sun but does not cool down easily at night

(iv).  The roots for the equation x + 10 = 3x2 are x = 3 and x = 2

 

Sol:

(i)  Here ‘and’ is a connecting word. Here component statements will be:

a: Every real number is not complex.

b: Every rational number are real.

 

(ii)  Here, ‘or’ is a connecting word. Here component statements will be:

a: Square of any integer is negative.

b: Square of any integer is positive.

 

(iii)  Here ‘but’ is connecting word. Here component statements will be:

a: The sand heats up easily due to sun.

b: The sand dose not cool down easily at night.

 

(iv)  Here ‘and’ is the connecting word. Here component statements will be:

a: The roots for the equation x + 10 = 3x2 are x = 3

b: The roots for the equation x + 10 = 3x2 are x = 2

 

 

Q.2: Write negation for the statements after identifying the quantifier for the statements

(i).  There exits one number that is equal to the square of the number

(ii).  For every number that is real ‘x’, x < x + 1

(iv).  There exist one capital for each state of India.

Sol:

(i) The quantifier will be “There exist” and negation for the statement is:

There doesn’t exist any number that is equal to the square of the number.

 

(ii) The quantifier will be “ For every” and negation for the statement is:

There exist a number x that is not less than x + 1

 

(iii) The quantifier will be “There exist” and negation for the statement is:

There exist one state that has no capital.

 

Q.3: Check if the following statements are negation for each other. Justify your answer

(i).  y + x = x + y is true for real numbers x and y

(ii).  There exist real numbers x, y such that y + x = x + y

 

Sol:

The negation for statement (i) will be:

There exist real numbers x, y such that y + x ≠ x + y, which is not statement (ii).

So the statements are not negation for each other.

 

 

Q.4: State if the “Or” in the statements is inclusive or exclusive. Justify the answer

(i) Moon sets or sun rises

(ii) You must have ration card or passport for applying a driving license.

(iii) Integers are negative or positive

 

Sol:

(i) “or” is exclusive as it is impossible for moon to set and sun to rise together.

(ii) “or” is inclusive as one can have both passport and ration card for applying a driving license.

(iii) “or” is exclusive as integers can’t be negative and positive.

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