Let A={1,3,7,9,11} and B={2,4,5,7,8,10,12}. T | vedclass

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(D) Given sets are $A=\{1,3,7,9,11\}$ and $B=\{2,4,5,7,8,10,12\}$.We need to find the number of one-one functions $f: A \rightarrow B$ such that $f(1)

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$240$

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(D) Given sets are $A=\{1,3,7,9,11\}$ and $B=\{2,4,5,7,8,10,12\}$.We need to find the number of one-one functions $f: A ightarrow B$ such that $f(1)+f(3)=14$.The possible pairs $(f(1), f(3))$ from set $B$ such that their sum is $14$ are:$(i) (2, 12)$$(ii) (12, 2)$$(iii) (4, 10)$$(iv) (10, 4)$There are $4$ such pairs.For each pair,we have fixed the images of $2$ elements ($1$ and $3$) of set $A$.Now,we need to map the remaining $3$ elements of set $A$ (i.e.,${7, 9, 11}$) to the remaining $5$ elements of set $B$ (since $7-2=5$ elements are left in $B$).The number of ways to map these $3$ elements one-one is given by the permutation formula $P(5, 3) = 5 	imes 4 	imes 3 = 60$.Therefore,the total number of one-one functions is $4 	imes 60 = 240$.

Let $A=\{1,3,7,9,11\}$ and $B=\{2,4,5,7,8,10,12\}$. Then the total number of one-one maps $f: A \rightarrow B$,such that $f(1)+f(3)=14$,is:

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