Identify the domain and the range of the relation
- (2, 5), (5, 11), (7, 15), (8, 17)
- (-2, -1), (-1, -3), (0, -5), (1, -7)
3) (12, 1), (10, 3), (8, 5), (6, 7)
4) (-4, -2), (-6, -3), (-8, -4), (-10, -5)
Answer :
Relation : A relation R over a set X is a set of ordered pair (x, y) where x and y are elements of X. We say x is related to y if (x, y) belongs to R.
Domain of the relation : The set of all first point of the pair (x,y) belonging to the relation is called domain of the relation.
Range of the relation : The set of all second point of the pair (x,y) belonging to the relation is called range of the relation.
For the first relation (2, 5), (5, 11), (7, 15), (8, 17)
Domain : {2,5,7,8}
Range : {5,11,15,17}
For the second relation (-2, -1), (-1, -3), (0, -5), (1, -7)
Domain : {-2,-1,0,1}
Range : {-1,-3,-5,-7}
For the thirs relation (12, 1), (10, 3), (8, 5), (6, 7)
Domain : {12,10,8,6}
Range : {1,3,5,7}
For the fourth relation (-4, -2), (-6, -3), (-8, -4), (-10, -5)
Domain : {-4,-6,-8,-10}
Range : { -2,-3,-4,-5}
Is the relation a function ?
- {(5,-5),(-6,9),(5,3),(-2,8),(-1,7)}
- {(-2,0),(-1,4),(0,8),(-1,6),(-5,5)}
- {(1,5),(0,8),(2,0),(3,4),(4,6)}
- {(-9,9),(7,8),(-5,5),(7,8),(-6,6)}
Answer :
Function : A relation R is said to be a function if the each element of the domain is mapped to a unique element of the range.
- For the relation {(5,-5),(-6,9),(5,3),(-2,8),(-1,7)}. 5 has two images -5 and 3. Therefore this relations is not a function.
2. For the relation {(-2,0),(-1,4),(0,8),(-1,6),(-5,5)} . -1 has two images 4 and 6. Therefore this relation is also not a function.
3. For the relation {(1,5),(0,8),(2,0),(3,4),(4,6)}. Each element of the domain has unique image in the range. Therefore it is a function.
4. For the relation {(-9,9),(7,8),(-5,5),(7,8),(-6,6)}. Each element of the domain has unique image in the range. Therefore it is a function.