Question

off. 9. Is R= [(-5, a),(1, a),(3,b), (4,C),(3,c)} is a function R from X to Y or not. Give reason. Given that X = (-5,1,3,4} and Y = {a,b,c}.​

Answer 1

Answer:

A={1,2,3,4} and B={1,5,9,11,15,16}

A={1,2,3,4} and B={1,5,9,11,15,16}∴A×B={(1,1),(1,5),(1,9),(1,11),(1,15),(1,16),(2,1),(2,5),(2,9),(2,11),(2,15),(2,16),

A={1,2,3,4} and B={1,5,9,11,15,16}∴A×B={(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)}

A={1,2,3,4} and B={1,5,9,11,15,16}∴A×B={(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)}It is given that f={(1,5),(2,9),(3,1),(4,5),(2,11)}

A={1,2,3,4} and B={1,5,9,11,15,16}∴A×B={(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)}It is given that f={(1,5),(2,9),(3,1),(4,5),(2,11)}(i) A relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A×B

A={1,2,3,4} and B={1,5,9,11,15,16}∴A×B={(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)}It is given that f={(1,5),(2,9),(3,1),(4,5),(2,11)}(i) A relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A×BIt is observed that f is a subset of A×B

A={1,2,3,4} and B={1,5,9,11,15,16}∴A×B={(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)}It is given that f={(1,5),(2,9),(3,1),(4,5),(2,11)}(i) A relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A×BIt is observed that f is a subset of A×BThus f is a relation from A to B.

(ii) Since the element 2 corresponds to two different images i.e., 9 and 11. So, relation f is not a function

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