Sets Questions

What are Universal Relation with Example ?

Solution : Let A be a set. Then, A \(\times\) A \(\subseteq\) A \(\times\) A and so it is a relation on A. This relation is called the universal relation on A. In other words, a relation R on a set is called universal relation, if each element of A is related to every element โ€ฆ

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What is Void or Empty Relation with Example ?

Solution : Let A be a set. Then, \(\phi\) \(\subseteq\) A \(\times\) A and so it is a relation on A. This relation is called the void or empty relation on set A. In other words, a relation R on a set A is called void or empty relation, if no element of A is โ€ฆ

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Prove that the total number of subsets of a finite set containing n elements is \(2^n\).

Solution : Let A be a finite set containing n elements. Let 0 \(\le\) r \(\le\) n. Consider those subsets of A that have r elements each. We know that the number of ways in which r elements can be chosen out of n elements is \(^nC_r\). Therefore, the number of subsets of A having โ€ฆ

Prove that the total number of subsets of a finite set containing n elements is \(2^n\). Read More ยป

What is Singleton Set ?

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.

Let A and B be two sets containing 2 elements and 4 elements, respectively. The number of subsets A\(\times\)B having 3 or more elements is

Solution : Given, n(A) = 2 and n(B) = 4 \(\therefore\) n(A\(\times\)B) = 8 The number of subsets of (A\(times\)B) having 3 or more elements = \(^8C_3 + {^8C_4} + โ€ฆ.. + {^8C_8}\) = \(2^8 โ€“ {^8C_0} โ€“ {^8C_1} โ€“ {^8C_2}\) = 256 โ€“ 1 โ€“ 8 โ€“ 28 = 219     [\(\because\) \(2^n\) = โ€ฆ

Let A and B be two sets containing 2 elements and 4 elements, respectively. The number of subsets A\(\times\)B having 3 or more elements is Read More ยป

If A = {x,y}, then the power set of A is

Solution : Clearly P(A) = Power set of A = set of all subsets of A = {\(\phi\), {x}, {y}, {x,y}} Similar Questions Let A and B be two sets containing 2 elements and 4 elements, respectively. The number of subsets A\(\times\)B having 3 or more elements is If aN = {ax : x \(\in\) โ€ฆ

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