Question:

The number of onto mappings from the set A = {1, 2, ....., 100} to set B = {1, 2} is:

Updated On: Mar 21, 2025
  • $2^{100} - 2 $
  • $2^{100} $
  • $2^{99} - 2 $
  • $2^{99} $
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The Correct Option is A

Solution and Explanation

The total no. of elements in A = 100. And the total no. of elements in B = 2. Hence no. of possible onto mapping in $2^{100}$. But this also contain the no. of elements in B differently, thus the total no. of possible onto mapping from the set A to set B is $2^{100} - 2$.
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Notes on types of relations

Concepts Used:

Types of Relation

TYPES OF RELATION

Empty Relation

Relation is said to be empty relation if no element of set X is related or mapped to any element of X i.e, R = Φ.

Universal Relation

A relation R in a set, say A is a universal relation if each element of A is related to every element of A.

R = A × A.

Identity Relation

Every element of set A is related to itself only then the relation is identity relation.

Inverse Relation

Let R be a relation from set A to set B i.e., R ∈ A × B. The relation R-1 is said to be an Inverse relation if R-1 from set B to A is denoted by R-1

Reflexive Relation

If every element of set A maps to itself, the relation is Reflexive Relation. For every a ∈ A, (a, a) ∈ R.

Symmetric Relation

A relation R is said to be symmetric if (a, b) ∈ R then (b, a) ∈ R, for all a & b ∈ A.

Transitive Relation

A relation is said to be transitive if, (a, b) ∈ R, (b, c) ∈ R, then (a, c) ∈ R, for all a, b, c ∈ A

Equivalence Relation

A relation is said to be equivalence if and only if it is Reflexive, Symmetric, and Transitive.