Number of Elements in a Cartesian Product
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Suppose that the number of elements in set is , the number of elements in set is and the number of elements in is . Then
A and B are two sets given in such a way that (A×B) contains 6 elements. If three elements of (A×B) be (1, 3), (2, 5) and (3, 3), find its remaining elements.
What does mean in ?
- 4
- 16
- 8
- 12
If the Cartesian product A × A has 16 elements among which few elements are found to be (-1, 0), (0, 1), (1, 2). Find set A.
{-1, 0, 2, 3}
{-1, 0, 1}
{-1, 0, 1, 2}
{0, 1, 2, 3}
Let be a set with elements. The number of onto functions from to is?
- B={x:x2−8x+15=0}
- B={x:|x−4|=1}
- B={x:x is prime factor of 15}
- B={x:x∈N, 3≤x≤5}
- 10
- 11
- 12
- 13
- 25
- infinite
- 16
- 9
- A={−3, 2}
- B={−2, 4}
- A×B={(−3, −2), (2, −2), (4, −2), (−3, 4), (2, 4), (4, 4)}
- B×A={(−2, −3), (−2, 2), (4, −3), (4, 2)}
If set A = {1, 2, 3} and set B = {2, 3, 5, 7}. Find the number of elements in A × B.
Suppose A1, A2, .....................A30 are thirty sets each having 5 elements and B1, B2, ................Bn are n sets each with 3 elements, let 30⋃i=1Ai=n⋃j=1Bj = S and each element of S belongs to exactly 10 of Ai'S and exactly 9 of the Bj'S. Then n is equal to
15
50
3
45
- Pq
- pq
- p×q
- qp
If set A has p element and set B has q element number of element in set (A × B) is _____.
- 24
- 36
- 12
- 16
- 6
- 12
- 1
- 24
B={x:x is a positive even number, x<14} and C={1, 4, 8}, then n((A×B)∩(A×C)) is
- 40
- 8
- 20
- 36
If set A = {1, 2, 3} and set B = {2, 3, 5, 7}. Find the number of elements in A × B.
If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A×B).
The least value of expression x2+4y2+9z2 - 2x + 8y + 27z + 15 is :
15
5
0
None
If A and B are subsets of the universal set U, then show that:-
(i) AsubsetAUB
(ii) AsubsetBAUB=B
If set A has p element and set B has q elements, then the number of element in set (A × B) is _____.
A × A × A has 512 elements. Find the number of elements in A.
- 1
- 2
- 4
- 8
Given two finite sets A and B such that n(A) = 3, n(B) = 3. Then total number of relations from A to B is _____.
8
4
512
6