Let A-a-b-c and B-1-2-3-4- Then the number of elements in the set C - f- A- B - 2 - fA and f is not one-one is

C = { f: A→ B | 2 nbsp; ∈ f(A) and f is not one–one} Case I: If f(x) = 2 ∀ nbsp; x ∈ A, then number of function = 1. Case II : If f(x) = 2 for exactly t ...

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Standard XII

Mathematics

Continuity in an Interval

Let A=a,b,c a...

Question

Let $A = {a, b, c}$ and $B = {1, 2, 3, 4}$ . Then the number of elements in the set $C = {f : A \to B | 2 \in f (A) and f is not one-one}$ is

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19.00

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19.0

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Solution

$C = {f : A \to B | 2 \in f (A) and f is not one-one}$
Case-I: If $f (x) = 2 \forall x \in A,$ then number of function $= 1.$
Case-II : If $f (x) = 2$ for exactly two elements then total number of many-one function.
$=^{3} C_{2} \times^{3} C_{1} = 9$
$Case-III : If f (x) = 2 for exactly one elements then total number of many-one function$
$=^{3} C_{1} \times^{3} C_{1} = 9$
Total $= 1 + 9 + 9 = 19$

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Similar questions

Let $A = \{a, b, c\}$ and $B = \{1, 2, 3, 4\}$ . Then the number of elements in the set $C = \{f : A \to B | 2 \in f (A) and f isnotone-one\}$ is

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Let A={a,b,c} and B={1,2,3,4}. Then the number of elements in the set C={f:A→B | 2∈f(A) and f is not one–one} is

Let $A = {a, b, c}$ and $B = {1, 2, 3, 4}$ . Then the number of elements in the set $C = {f : A \to B | 2 \in f (A) and f is not one-one}$ is