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  • Let A ={1,2,3,4}, B = {1,5,9,11,15,16} and f = {(1,5), (2,9), (3,1), (4,5), (2,11)} Are the following true? f is a relation from A to B

Q10 (1)  Let A ={1,2,3,4}, B = {1,5,9,11,15,16} and f = {(1,5), (2,9), (3,1), (4,5), (2,11)}
               Are the following true?  f is a relation from A to B

Answers (1)

best_answer

It is given that 
A =\left \{ {1,2,3,4} \right \} 
B =\left \{ {1,5,9,11,15,16} \right \} 
and f =\left \{ {(1,5), (2,9), (3,1), (4,5), (2,11)} \right \}
Now,
A \times B =\left \{ (1,1), (1,5), (1,9), (1,11), (1,15), (1,16), (2,1), (2,5), (2,9), (2,11), (2,15), (2,16), (3,1), (3,5), (3,9), (3,11), (3,15), (3,16), (4,1), (4,5), (4,9), (4,11), (4,15), (4,16) \right \}Now, a relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A × B
And we can see that f is a subset of A \times B
Hence  f is a relation from A to B 
Therefore, given statement is TRUE

Posted by

Gautam harsolia

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