Universal Set
Trending Questions
Q. Let Z be the set of all integers.
A={(x, y)∈Z×Z:(x−2)2+y2≤4},
B={(x, y)∈Z×Z:x2+y2≤4} and
C={(x, y)∈Z×Z:(x−2)2+(y2−2)2≤4}
If the total number of relations from A∩B to A∩C is 2p, then the value of p is
A={(x, y)∈Z×Z:(x−2)2+y2≤4},
B={(x, y)∈Z×Z:x2+y2≤4} and
C={(x, y)∈Z×Z:(x−2)2+(y2−2)2≤4}
If the total number of relations from A∩B to A∩C is 2p, then the value of p is
- 16
- 49
- 25
- 9
Q.
If U= {2, 3, 5, 7, 9} is the universal set and A = {3, 7} , B = {2, 5, 7, 9}, then prove that :
(i) A∪B)′=A′∩B′
(ii) A∩B)′=A′∪B′
Q. Which of the following is not correct?
- A=C is equivalent to A∪B=B∪C and A∩B=B∩C
- AC⊆A⇔A=x where x is universal set
- If A∪B=A∪C, then B=C
- A⊆AC if and only if A=ϕ
Q. State which of the following sets are finite or infinite:
(i) {x:x ∈ N and (x−1)(x−2)=0}
(ii) {x:x ∈ N and x2=4}
(iii) {x:x ∈ N and 2x−1=0}
(iv) {x:x ∈ N and x is prime}
(v) {x:x ∈ N and x is odd}
(i) {x:x ∈ N and (x−1)(x−2)=0}
(ii) {x:x ∈ N and x2=4}
(iii) {x:x ∈ N and 2x−1=0}
(iv) {x:x ∈ N and x is prime}
(v) {x:x ∈ N and x is odd}
Q. Let A, B are two non-empty sets and U be the universal set. Then which of the following statements is/are true?
1. n(A∪B)′=n(A′∩B′)
2. If A∩B=ϕ, then A′∪B′=U
3. If A∪B=U, then A′∩B′=ϕ
4. If A⊂B, then A′∪B′=(A∩B)′
(where ϕ denote the null set)
1. n(A∪B)′=n(A′∩B′)
2. If A∩B=ϕ, then A′∪B′=U
3. If A∪B=U, then A′∩B′=ϕ
4. If A⊂B, then A′∪B′=(A∩B)′
(where ϕ denote the null set)
- 1, 2 and 3 only
- 1, 2 and 4 only
- All statements are true
- 1 and 3 only
Q.
If the set of has elements, then the total number of subsets of is:
Q. If A={1, 3, 5}, B={2, 4, 6}, C={1, 4} then which of the following is universal set?
- {0, 1, 2, 3, 4, 5}
- {1, 2, 3, 4, 6}
- ϕ
- {1, 2, 3, 4, 5, 6, 7, 8}
Q. The universal set of the following sets is
A is set of similar triangles
B is set of right-angled triangles
C is set of equilateral triangles
A is set of similar triangles
B is set of right-angled triangles
C is set of equilateral triangles
- The collection of all triangles
- The collection of all straight lines
- None of these
- The collection of all angles
Q. What universal set(s) would you propose for each of the following?
(i) The set of right triangles.
(ii) The set of isosceles triangles.
(i) The set of right triangles.
(ii) The set of isosceles triangles.
Q. Show that the function x+a-[x-b] is a periodic function. Find its period. (a and b are positive real numbers)
Q.
For any two sets of A and B, prove that :
(i) A′∪B=U⇒A⊂B
(ii) B′⊂A′⇒A⊂B
Q.
What universal set (s) would you propose for each of the following :
(i) The set of right triangles
(ii) The set of isosceles triangles
Q.
How many months does coordinate Geometry takes to cover in class 11 (approx) ?
Q. A set which contains all the elements of other given sets is called a ________ set.
- universal
- subset
- power
- proper
Q. Let A, B are two non-empty sets and U be the universal set. Then which of the following statements is/are true?
1. n(A∪B)′=n(A′∩B′)
2. If A∩B=ϕ, then A′∪B′=U
3. If A∪B=U, then A′∩B′=ϕ
4. If A⊂B, then A′∪B′=(A∩B)′
(where ϕ denote the null set)
1. n(A∪B)′=n(A′∩B′)
2. If A∩B=ϕ, then A′∪B′=U
3. If A∪B=U, then A′∩B′=ϕ
4. If A⊂B, then A′∪B′=(A∩B)′
(where ϕ denote the null set)
- 1, 2 and 3 only
- 1 and 3 only
- 1, 2 and 4 only
- All statements are true
Q. Write down all the subsets of the set {1, 2, 3}
Q.
If, show that