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

If A and B are two sets, then A ∩ (A ∪ B) equals ______.

If X and Y are two sets and X′ denotes the complement of X, then X ∩ (X ∪ Y)′ is equal to ______.

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 5}, B = {2, 4, 6, 7} and C = {2, 3, 4, 8}. Then (B ∪ C)′ is ______.

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 5}, B = {2, 4, 6, 7} and C = {2, 3, 4, 8}. Then (C – A)′ is ______.

Find the intersection of pair of sets:

X = {1, 3, 5}, Y = {1, 2, 3}

Find the intersection of pair of sets:

A = {a, e, i, o, u}, B = {a, b, c}

Find the intersection of pair of sets:

A = {x : x is a natural number and multiple of 3}

B = {x : x is a natural number less than 6}

Find the intersection of pair of sets:

A = {x : x is a natural number and 1 < x ≤ 6}

B = {x : x is a natural number and 6 < x < 10}

Find the intersection of pair of sets:

A = {1, 2, 3}, B = Φ

If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find

A ∩ B

If A = {x : x is a natural number}, B = {x : x is an even natural number} C = {x : x is an odd natural number} and D = {x : x is a prime number}, find:

A ∩ B

Let A, B and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C. Show that B = C.

Show that the following four conditions are equivalent:

1. A ⊂ B
2. A – B = Φ
3. A ∪ B = B 
4. A ∩ B = A

Using properties of sets show that A ∪ (A ∩ B) = A

Using properties of sets show that A ∩ (A ∪ B) = A.

Show that A ∩ B = A ∩ C need not imply B = C.

Let A and B be sets. If A ∩ X = B ∩ X = Φ and A ∪ X = B ∪ X for some set X, show that A = B.

(Hints A = A ∩ (A ∪ X), B = B ∩ (B ∪ X) and use distributive law)

In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

Find the eccentricity of an ellipse whose latus rectum is  half of its minor axis  

Find the eccentricity of an ellipse whose latus rectum is  half of its major axis.