Let and . A relation from to is specified by the assignments 1 a, ;1 b, ;2 c, ;3 c,…

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

M=\{1,2,3,4,5\}

and

N=\{a,b,c,d\}

. A relation

R

from

M

N

is specified by the assignments

1\mapsto a,\;1\mapsto b,\;2\mapsto c,\;3\mapsto c,\;4\mapsto d,\;5\mapsto d.

(i) Represent

R

by a mapping diagram. (ii) Determine whether

R

is a function from

M

N

, giving reasons based on your diagram. (iii) Find all subsets

F

R

such that

F

is a function

F: M^{\prime}\to N

where

M^{\prime}\subseteq M

and

|M^{\prime}|\ge 4

. List each such subset explicitly and justify that it satisfies the definition of a function.