Question

If A = {1, 2, 3}, find the relation on A satisfying the condition x+y<4. Is this relation a function? Give reason.

Answer 1

Answer:

For function, every element of the domain must have a unique image in co-domain...

(A)Let us redefine each function as a set of ordered pairs 

and see if they satisfy the above condition (A) of a function f1={(1,2),(2,3),(3,4)} ; (4,5) cannot be an ordered pair as 5 does not belong to co-domain , Thus the element 4 of domain does not have an image.

f2={(1,4),(2,3),(2,4),(3,2)(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}

The uniqueness is violated as the elements have not one but many images.

f3={(2,1),(3,2),(3,1),(4,1),(4,2),(4,3)} Not a function as in f2 uniqueness is violated. 

f4={(1,4),(2,3),(3,2)(4,1)} It is a function as each element has a unique image.

Answer 2

Answer:

A = {1, 2, 3}, find the relation on A satisfying the condition x+y<4. Is this relation a function? Give reason.