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

Show that for any sets A and B, A = (A ∩ B) ∪ (A – B) and A ∪ (B – A) = (A ∪ B)

From the data given below state which group is more variable, A or B?

We have to find the smallest set A such that\[A \cup \left\{ 1, 2 \right\} = \left\{ 1, 2, 3, 5, 9 \right\}\] 

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identities: 

\[A \cup \left( B \cap C \right) = \left( A \cup B \right) \cap \left( A \cup C \right)\]

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identitie:

\[A \cap \left( B \cup C \right) = \left( A \cap B \right) \cup \left( A \cap C \right)\]

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identitie:

\[A \cap \left( B - C \right) = \left( A \cap B \right) - \left( A \cap C \right)\]

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identitie: 

\[A - \left( B \cup C \right) = A\left( A - B \right) \cap \left( A - C \right)\] 

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identitie: 

\[A - \left( B \cap C \right) = \left( A - B \right) \cup \left( A - C \right)\] 

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identitie:

\[A \cap \left( B ∆ C \right) = \left( A \cap B \right) ∆ \left( A \cap C \right)\]

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

A ∪ C

Each set X_r contains 5 elements and each set Y_r contains 2 elements and \[\bigcup\limits_{r=1}^{20} X_{r} = S = \bigcup\limits_{r=1}^{n} Y_{r}\] If each element of S belong to exactly 10 of the X_r’s and to exactly 4 of the Y_r’s, then n is ______.

Given L = {1, 2, 3, 4}, M = {3, 4, 5, 6} and N = {1, 3, 5}. Verify that L – (M ∪ N) = (L – M) ∩ (L – N)

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

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

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 ⊂ 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