Commerce (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

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"}.

From the sets given below, select equal sets and equivalent sets.
A = {0, a}, B = {1, 2, 3, 4} C = {4, 8, 12}, D = {3, 1, 2, 4},
E = {1, 0}, F = {8, 4, 12} G = {1, 5, 7, 11}, H = {a, b}. 

Which of the following sets are equal?
A = {x : x ∈ N, x, < 3},
B = {1, 2}
C = {3, 1}
D = {x : x ∈ N, x is odd, x < 5},
E = {1, 2, 1, 1} F = {1, 1, 3}. 

Show that the set of letters needed to spell "CATARACT" and the set of letters needed to spell "TRACT" are equal. 

The function f is defined by

For any set A, (A')' is equal to 

The set  \[\left( A \cup B' \right)' \cup \left( B \cap C \right)\] is equal to