Number of Onto, Into & Constant Functions from A to B

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SUMMARY

The discussion focuses on calculating the number of onto, into, and constant functions from set A, which contains six elements {1, 2, 3, 4, 5, 6}, to set B, which contains five elements {a, b, c, d, e}. The total number of onto functions can be determined using the inclusion-exclusion principle. For into functions, the total is calculated as 5^6, representing all possible mappings from A to B. A constant function is defined as a function that maps every element of A to a single element in B.

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If $A = \left\{1,2,3,4,5,6\right\}$ and $B = \left\{a,b,c,d,e\right\}$. Then Total no. of $(1)$ onto function from $A$ to $B$$(2)$ into function from $A$ to $B$$(3)$ Constant function from $A$ to $B$Plz explain it breifly"Thanks"
 
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jacks said:
If $A = \left\{1,2,3,4,5,6\right\}$ and $B = \left\{a,b,c,d,e\right\}$. Then Total no. of
$(1)$ onto function from $A$ to $B$
$(2)$ into function from $A$ to $B$
$(3)$ Constant function from $A$ to $B$

For #1 use inclusion/exclusion to figure the answer.

In #2 how is into used? There are $5^6$ functions from a set six to a set of five.

For #3 think what it means to be a constant function.
 

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