Here you will learn definition of equal sets and equivalent sets with examples. Let’s begin – Equal Sets and Equivalent Sets (i) Equal Sets : Two finite sets A and B are equivalent if their cardinal numbers are same i.e. n(A) = n(B). Where cardinal number means numbers of elements in a set. (ii) Equivalent …
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Here you will learn what are finite and infinite sets, cardinality of a finite set and examples based on it. Let’s begin – Finite and Infinite Sets (i) Finite Sets A set is called a finite set if it is either void set or its element can be listed (counted, labelled) by natural numbers 1, …
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Solution : A set consisting of a single element is called a singleton set. Example : The set {5} is a singleton set. Example : The set {x : x \(\in\) N and \(x^2\) = 9} is a singleton set equal to {3}. Note : The cardinal number of a singleton set is 1.
Solution : The cardinality of a set is the number of elements in a set. For example : Let A be a set : A = {1, 2, 4, 6} Set A contains 4 elements. Therefore, Cardinality of set is 4.
Here you will learn what is an empty set in math, its symbol and definition with examples. Let’s begin – What is the Empty Set in Math ? Definition : A set is said to be empty set if it has no element. It is also called null or void set. It is denoted by …
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Here you will learn what is set builder form and how to represent sets in set builder form with examples. Let’s begin – Set Builder Form Definition : In this form, a set is described by a characterizing property P(x) of its elements x. In such a case the set is described by {x : …
Here you will learn what is roster form in sets and how to represent sets in roaster form with examples. Let’s begin – Roster Form in Sets Definition : In this method a set is described by listing elements, separated by comma and enclose then by curly brackets { }. Example 1 : The set …
Solution : The general solution of \(tan \theta\) = \(tan \alpha\) is given by \(\theta\) = \(n\pi + \alpha\), n \(\in\) Z. Proof : We have, \(tan \theta\) = \(tan \alpha\) \(\implies\) \(sin \theta\over cos \theta\) = \(sin \alpha\over cos \alpha\) \(\implies\) \(sin \theta cos \alpha\) – \(cos \theta sin \alpha\) = 0 \(\implies\) \(sin …
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Solution : The general solution of \(cos \theta\) = \(cos \alpha\) is given by \(\theta\) = \(2n\pi \pm \alpha\), n \(\in\) Z. Proof : We have, \(cos \theta\) = \(cos \alpha\) \(\implies\) \(cos \theta\) – \(cos \alpha\) = 0 \(\implies\) -\(2 sin ({\theta + \alpha\over 2}) sin({\theta – \alpha\over 2})\) = 0 \(\implies\) \(sin ({\theta …
What is the General Solution of \(cos \theta\) = \(cos \alpha\) ? Read More »
Solution : The general solution of \(sin \theta\) = \(sin \alpha\) is given by \(\theta\) = \(n\pi + (-1)^n \alpha\), n \(\in\) Z. Proof : We have, \(sin \theta\) = \(sin \alpha\) \(\implies\) \(sin \theta\) – \(sin \alpha\) = 0 \(\implies\) \(2 sin ({\theta – \alpha\over 2}) cos({\theta + \alpha\over 2})\) = 0 \(\implies\) \(sin …
What is the General Solution of \(sin \theta\) = \(sin \alpha\) ? Read More »
