Arts (English Medium) इयत्ता ११ - CBSE Question Bank Solutions

Write each of the following statement in the form “if-then”.

To get A⁺ in the class, it is necessary that you do the exercises of the book.

Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other.

(a) If you live in Delhi, then you have winter clothes.

(i) If you do not have winter clothes, then you do not live in Delhi.

(ii) If you have winter clothes, then you live in Delhi.

(b) If a quadrilateral is a parallelogram, then its diagonals bisect each other.

(i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.

(ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

State the converse and contrapositive of each of the following statements:

p: A positive integer is prime only if it has no divisors other than 1 and itself.

State the converse and contrapositive of each of the following statements:

q: I go to a beach whenever it is a sunny day.

State the converse and contrapositive of each of the following statements:

r: If it is hot outside, then you feel thirsty.

Write the statement in the form “if p, then q”.

r: You can access the website only if you pay a subscription fee.

Re write each of the following statements in the form “p if and only if q”.

p: If you watch television, then your mind is free and if your mind is free, then you watch television.

Re write each of the following statements in the form “p if and only if q”.

q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.

Re write each of the following statements in the form “p if and only if q”.

r: If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

Given below are two statements

p: 25 is a multiple of 5.

q: 25 is a multiple of 8.

Write the compound statements connecting these two statements with “And” and “Or”. In both cases check the validity of the compound statement.

If A = {1, 2, 4} and B = {1, 2, 3}, represent set graphically:
(i) A × B

If A = {1, 2, 4} and B = {1, 2, 3}, represent set graphically: 

(ii) B × A

If A = {1, 2, 4} and B = {1, 2, 3}, represent set graphically:

(iii) A × A

If A = {1, 2, 4} and B = {1, 2, 3}, represent set graphically:

(iv) B × B 

Which of the following sets are equal?

\[A = \left\{ 1, 2, 3 \right\};\]

Which of the following sets are equal? 

(i) \[A = \left\{ 1, 2, 3 \right\};\] 

(ii) \[B = \left\{ x \in R : x^2 - 2x + 1 = 0 \right\};\] 

(iii) \[C = \left\{ 1, 2, 2, 3 \right\};\] 

(iv) \[D = \left\{ x \in R : x^3 - 6 x^2 + 11x - 6 = 0 \right\}\]

Are the following sets equal?
A = {x : x is a letter in the word reap}:
B = {x : x is a letter in the word paper};
C = {x : x is a letter in the word rope}.

From the sets given below, pair the equivalent sets: 

\[A = \left\{ 1, 2, 3 \right\}, B = \left\{ t, p, q, r, s \right\}, C = \left\{ \alpha, \beta, \gamma \right\}, D = \left\{ a, e, i, o, u \right\} .\]

Are the following pairs of sets equal? Give reasons. 

A = {2, 3}, B = {x : x is a solution of x² + 5x + 6 = 0}

Are the following pairs of sets equal? Give reasons. 

A = {x : x is a letter of the word " WOLF"};
    B = {x : x is a letter of the word " FOLLOW"}.