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Standard XII

Mathematics

One - One function

For a functio...

Question

For a function $f : A \to B$ , the number of elements in set $A$ and $B$ are $5$ and $4$ respectively, then the number of many one functions are

1024.00

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1024

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1024.0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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Solution

Here, we have $n (A) = 5$ and $n (B) = 4.$
So, total number of functions $= 4 \times 4 \times 4 \times 4 \times 4 = 4^{5}$
Number of one-one functions $= 0 (∵ n (A) > n (B))$
$∴$ Number of many one functions $=$ total functions $-$ one-one functions
$= 1024 - 0 = 1024$

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One - One function

Standard XII Mathematics

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For a function f:A→B, the number of elements in set A and B are 5 and 4 respectively, then the number of many one functions are

Here, we have n(A)=5 and n(B)=4. So, total number of functions =4×4×4×4×4=45 Number of one-one functions =0 (∵n(A)>n(B)) ∴ Number of many one functions = total functions − one-one functions =1024−0=1024

For a function $f : A \to B$ , the number of elements in set $A$ and $B$ are $5$ and $4$ respectively, then the number of many one functions are

Here, we have $n (A) = 5$ and $n (B) = 4.$
So, total number of functions $= 4 \times 4 \times 4 \times 4 \times 4 = 4^{5}$
Number of one-one functions $= 0 (∵ n (A) > n (B))$
$∴$ Number of many one functions $=$ total functions $-$ one-one functions
$= 1024 - 0 = 1024$