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If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is

\begin{array}{1 1}(A)\quad 720 & (B)\quad 120\\(C)\quad 0 & (D)\quad none\; of\; these\;\end{array}

1 Answer

  • 1. A mapping from A to B is one-one
  • if $f(a)=f(b) \qquad a,b \in A$
  • $=> a=b$
  • 2.For every element $y \in B$ there exists an element $ x \in A$ such that $f(x)=y$
  • 3.For a mapping to be both one-one and onto. the number of elements of A and B should be equal or a
  • B subset of A
A has 5 elements
B has 6 elements
Since mumber of elements in B is more than A there cannot be any one-one and onto mapping from A to B
Solution:'c' option is correct
answered Mar 5, 2013 by meena.p
edited Mar 27, 2013 by meena.p

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