Consider the two class classification task that consists of the following points:
Class $C_1$: [-1, -1], [-1, 1], [1, -1]
Class $C_2$: [1,1]
The decision boundary between the two classes $C_1$ and $C_2$ using single perception is given by:
It assumes a sign function, i.e try replacing x and y, the equation which classifies the dataset properly is the right answer.
e.g for case four.
-1 -1 -.5 = -2.5 since it turned out negative call it Class C1
-1+1 -.5=-.5 class C1
1-1-.5=-.5 class C1
1+1-.5-=1.5 since this is positive call it C2
Note: option D is the only equation that classifies them properly hence the answer.
ans is D