Let X={1,2,3} and Y={4,5}.Find whether the following subsets of X x Y are functions from X to Y or not.$\quad f=\{(1,4),(1,5),(2,4),(3,5)\} $

Question

Note: This is part 1 of a 4 part question, split as 4 separate questions here.

Answer 1

Toolbox:

• The given set of ordered pair subset of $x \times y$ function if same element $a \in x$ is not mapped on to two different elements of y
• The subset of $x \times $ is a function if it defines a mapping for each element of x an element of y

(i) $f=\{(1,4), and (1,5),(2,4),(3,5)\}$

 

Since (1,4) and (1,5) both belong to f the same element $1 \in X$ is mapped to two different elements in y, f is not a function.

hence f is not a function.