Advertisements
Advertisements
Question
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
Options
True
False
Solution
This statement is True.
Explanation:
Let x ∈ A ∪ B
⇒ x ∈ A or x ∈ B
⇒ x ∈ C or x ∈ B ......[∵ A ⊂ C and B ⊂ C]
⇒ x ∈ C
⇒ A ∪ B ⊂ C
APPEARS IN
RELATED QUESTIONS
Find the union of the following pairs of sets:
A = {a, e, i, o, u}, B = {a, b, c}
Find the union of the following pairs 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 union of the following pairs 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 union of the following pairs of sets:
A = {1, 2, 3}, B = Φ
If A and B are two sets such that A ⊂ B, then what is A ∪ B?
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find
A ∪ B
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:
\[A \cap \left( B - C \right) = \left( A \cap B \right) - \left( A \cap C \right)\]
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
Observe the given Venn diagram and write the following sets.
- A
- B
- A ∪ B
- U
- A'
- B'
- (A ∪ B)'
Each set Xr contains 5 elements and each set Yr 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 Xr’s and to exactly 4 of the Yr’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
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 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 ______.
