Question

Which set of ordered pairs is a function? {(1,1),(2, 2), (3, 3), (4,4), (5,5)} {(0,0),(1,1),(1, -1),(4,2),(4, -2)} {(2,1),(2,2).(2,3),(2,4),(2,5)} {(1,5).(2.4),(3,3).(2, 2), (1,1)​

Answer 1

`\underline{ \underline{ \large{ \red{ \tt{✧ E\: X \: P \: L \: A \: N \: A \: T\: I \:O\: N}}}}} :`

❀ Here, We are given relation from A to B [ Suppose ] & We have to identify whether they are function or not from the relation A to B.

• { ( 1 , 1 ) , (2 , 2 ) , ( 3 , 3 ) , (4 , 4 ) , ( 5 , 5 )}

⇢ This is a function from A to B because every element of Set A has unique image in set B.

• {( 0,0 ) , ( 1 , 1 ) , ( 1 , -1 ) , ( 4 , 2 ) , ( 4 , -2 ) }

⇢ This is not a function because two of the elements of Set A ( 1 & 4 ) are associated to elements -1 , 1 & 2 , -2 respectively of Set B

• { ( 2 , 1 ) , (2 , 2 ) , (2 , 3 ) , (2 , 4 ) , (2 , 5 )

⇢ This is not a function because the element of Set A ( 2 ) is associated to all the elements of Set B.

• { ( 1 , 5 ) , ( 2 , 4 ) , ( 3 , 3 ) , (2 , 2 ) , ( 1 , 1 )

⇢ This is not a function because the elements of Set A ( 1 & 2 ) are associated to elements ( 5 , 1 & 4 , 2 ) of Set B respectively.

`\boxed{ \boxed{ \large{ \purple{ \tt{A \: N \: S \: W \: E \: R: \{ ( 1 , 1 ) , (2 , 2 ) , ( 3 , 3 ) , (4 , 4 ) , ( 5 , 5 ) \} }}}}}`

♨ Q. What is function ? How can we identify whether the given relation is a function ?

⟶Function is a special type of relation. Function is the refinement of relation. In a relation from A to B , every element of Set A has only one ( distinct ) image in B. In other words , if no two different ordered pairs have the same first component , then it is a function.

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