Let A={1,2,3,4},B={x,y,z} Which of the following are relations from A to B?
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Answer:
Since every subset of A×B is a relation from A to B, therefore, R is also a relation
from A to B.
Domain of R={1,2,3}Range of R ={x,y,z}
Arrow diagram of R in the tabular form, we construct a box with the help of {n(A)+2} horizontal lines and {n(B)+2} vertical lines. In this case, we draw 6 horizontal lines and 5 vertical lines to get 20 boxes {n(A)+1}×{n(B)+1} in general). Place R in the extreme left top and elements of A below R in a vertical line. Write elements of B in the first horizontal line as shown.
As (1,x)∈R, place 1 in the row
containing x. As (1,z)∈
/
R, place 0 on the row containing 1 and column containing z. Complete the table corresponding to other pairs also. Here, we use the convention that if (a,b)∈R, we write '1' in the row containing a and column containing b and if (a,b)∈
Since every subset of A×B is a relation from A to B, therefore, R is also a relation
from A to B.
Domain of R={1,2,3}Range of R ={x,y,z}
Arrow diagram of R in the tabular form, we construct a box with the help of {n(A)+2} horizontal lines and {n(B)+2} vertical lines. In this case, we draw 6 horizontal lines and 5 vertical lines to get 20 boxes {n(A)+1}×{n(B)+1} in general). Place R in the extreme left top and elements of A below R in a vertical line. Write elements of B in the first horizontal line as shown.
As (1,x)∈R, place 1 in the row
containing x. As (1,z)∈
/
R, place 0 on the row containing 1 and column containing z. Complete the table corresponding to other pairs also. Here, we use the convention that if (a,b)∈R, we write '1' in the row containing a and column containing b and if (a,b)∈