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

Determine whether the following statement is true or false. Justify your answer.

For all sets A, B, and C, if A ⊂ B, then A ∪ C ⊂ B ∪ C

Determine whether the following statement is true or false. Justify your answer.

For all sets A, B, and C, if A ⊂ C and B ⊂ C, then A ∪ B ⊂ C

For all sets A and B, A ∪ (B – A) = A ∪ B

For all sets A and B, A – (A – B) = A ∩ B

For all sets A and B, A – (A ∩ B) = A – B

For all sets A and B, (A ∪ B) – B = A – B

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