Let A = { ( x , y ) : 2 x + 3 y = 23 , x , y ? N } and B = { x : ( x , y ) ? A } . Then the number of one-one functions from A to B is equal to ________ . [2024]

Question

Let $A = {(x, y) : 2 x + 3 y = 23, x, y \in N}$ and $B = {x : (x, y) \in A}$ . Then the number of one-one functions from A to B is equal to ________ . [2024]

Smart Achievers · Accepted Answer

(24)

We have, $A = {(x, y) : 2 x + 3 y = 23, x, y \in N}$

$B = {x : (x, y) \in A}$

$∴ A = {(1, 7), (4, 5), (7, 3), (10, 1)}$

and $B = {1, 4, 7, 10}$

Total number of one-one functions from A to B = 4! = 24

Solution

Q.
Let $A = {(x, y) : 2 x + 3 y = 23, x, y \in N}$ and $B = {x : (x, y) \in A}$ . Then the number of one-one functions from A to B is equal to ________ . [2024]

Ans.
(24)

We have, $A = {(x, y) : 2 x + 3 y = 23, x, y \in N}$

$B = {x : (x, y) \in A}$

$∴ A = {(1, 7), (4, 5), (7, 3), (10, 1)}$

and $B = {1, 4, 7, 10}$

Total number of one-one functions from A to B = 4! = 24

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Solution

Q. Let A={(x,y):2x+3y=23,x,y∈N} and B={x:(x,y)∈A}. Then the number of one-one functions from A to B is equal to ________ . [2024]

Ans. (24) We have, A={(x,y):2x+3y=23,x,y∈N} B={x:(x,y)∈A} ∴A={(1,7),(4,5),(7,3),(10,1)} and B={1,4,7,10} Total number of one-one functions from A to B = 4! = 24

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Q.
Let $A = {(x, y) : 2 x + 3 y = 23, x, y \in N}$ and $B = {x : (x, y) \in A}$ . Then the number of one-one functions from A to B is equal to ________ . [2024]

Ans.
(24)

We have, $A = {(x, y) : 2 x + 3 y = 23, x, y \in N}$

$B = {x : (x, y) \in A}$

$∴ A = {(1, 7), (4, 5), (7, 3), (10, 1)}$

and $B = {1, 4, 7, 10}$

Total number of one-one functions from A to B = 4! = 24