Advertisements
Advertisements
Question
What universal set (s) would you propose for the following:
The set of isosceles triangles.
Advertisements
Solution 1
The universal set for the set of isosceles triangles can be the set of triangles, polygons, or two-dimensional figures.
Solution 2
Isosceles triangle is a type of triangle. So the set of triangles contain all types of triangles.
∴ U = {x : x is a triangle in a plane)
APPEARS IN
RELATED QUESTIONS
What universal set (s) would you propose for the following:
The set of right triangles.
Given the sets, A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, the following may be considered as universal set (s) for all the three sets A, B and C?
{0, 1, 2, 3, 4, 5, 6}
Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, the following may be considered as universal set (s) for all the three sets A, B and C?
{1, 2, 3, 4, 5, 6, 7, 8}
If \[X = \left\{ 8^n - 7n - 1: n \in N \right\} \text{ and } Y = \left\{ 49\left( n - 1 \right): n \in N \right\}\] \[X \subseteq Y .\]
For three sets A, B and C, show that \[A \cap B = A \cap C\]
If A and B are sets, then prove that \[A - B, A \cap B \text{ and } B - A\] are pair wise disjoint.
Using properties of sets, show that for any two sets A and B,\[\left( A \cup B \right) \cap \left( A \cap B' \right) = A\]
For any two sets of A and B, prove that:
\[A' \cup B = U \Rightarrow A \subset B\]
For any two sets of A and B, prove that:
\[B' \subset A' \Rightarrow A \subset B\]
Show that for any sets A and B, A = (A ∩ B) ∪ ( A - B)
Show that for any sets A and B, A ∪ (B – A) = (A ∪ B)
For any two sets A and B, prove that :
\[A' - B' = B - A\]
For any two sets A and B, prove the following:
\[A \cap \left( A' \cup B \right) = A \cap B\]
For any two sets A and B, prove the following:
\[A - \left( A - B \right) = A \cap B\]
For any two sets A and B, prove the following:
\[A \cap \left( A \cup B \right)' = \phi\]
For any two sets A and B, prove the following:
\[A - B = A \Delta\left( A \cap B \right)\]
A survey shows that 76% of the Indians like oranges, whereas 62% like bananas. What percentage of the Indians like both oranges and bananas?
In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find: how many can speak Hindi only
In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find:
how many can speak English only.
Let A and B be two sets that \[n \left( A \right) = 16, n \left( B \right) = 14, n \left( A \cup B \right) = 25\] Then, \[n \left( A \cap B \right)\]
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find
B ∪ C
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find
B ∪ D
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 ∪ D
If X and Y are subsets of the universal set U, then show that Y ⊂ X ∪ Y
If X and Y are subsets of the universal set U, then show that X ∩ Y ⊂ X
If A and B are subsets of the universal set U, then show that A ⊂ A ∪ B
If A and B are subsets of the universal set U, then show that (A ∩ B) ⊂ A
Let A, B and C be sets. Then show that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
The set (A ∩ B′)′ ∪ (B ∩ C) is equal to ______.
