Question

Demonstrate your understanding of Map Algebra and logical operators by filling values to the empty cells. Operations are carried out from left to right. No zero values are considered True and zeros False. In the output, True is represented as 1, False 0

                Raster A                                          Raster B                                            Raster C

0	0	1				0	2	2				0	1	1
2	1	1				0	0	2				0	0	3
0	0	0				0	0	1				0	0	2

Map Algebra:

    (A - B)                                            (A+B+C)                                    (A*C) + (B*C)

Logical Operations:

   (A or B)                                           (A and C)                                     (A or (B and C))

Answer 1

Map algebra is pretty straightforward. We use the values for cells in the same location stored as different variables and perform the operations mentioned. Thus,

A - B is

0	-2	-1
2	1	-1
0	0	-1

A + B +C is

0	3	4
2	1	6
0	0	3

(A*C)+(B*C) is

0	2	3
0	0	9
0	0	2

The logical OR operator returns true if any one value is true, while AND returns true only if all values are true. Since non-zero values are true,

A or B is

0	1	1
1	1	1
0	0	1

In these cases, the value of true is specified as 1, therefore, we return a value of 1 whenever the statement is true.

A and C is

0	0	1
0	0	1
0	0	0

A or (B and C) is

0	1	1
1	1	1
0	0	1