Then the number of elements in the set {(n, m) : n, m ∈ { 1, 2….., 10} and nAn + mBm = I} is _______.
Then the number of elements in the set {(n, m) : n, m ∈ { 1, 2….., 10} and nAn + mBm = I} is _______.
Correct Answer: 1
Solution and Explanation
The correct answer is : 1
A2 = A and B2 = BR
nA + mB = I,
So, 2n – m = 1, –n + m = 0, 2m – n = 1
So, (m, n) = (1, 1)
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Concepts Used:
Types of Sets
Sets are of various types depending on their features. They are as follows:
- Empty Set - It is a set that has no element in it. It is also called a null or void set and is denoted by Φ or {}.
- Singleton Set - It is a set that contains only one element.
- Finite Set - A set that has a finite number of elements in it.
- Infinite Set - A set that has an infinite number of elements in it.
- Equal Set - Sets in which elements of one set are similar to elements of another set. The sequence of elements can be any but the same elements exist in both sets.
- Sub Set - Set X will be a subset of Y if all the elements of set X are the same as the element of set Y.
- Power Set - It is the collection of all subsets of a set X.
- Universal Set - A basic set that has all the elements of other sets and forms the base for all other sets.
- Disjoint Set - If there is no common element between two sets, i.e if there is no element of Set A present in Set B and vice versa, then they are called disjoint sets.
- Overlapping Set - It is the set of two sets that have at least one common element, called overlapping sets.