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+2 votes
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Which of the following 2 input Boolean logic functions is linearly inseparable ?

(a) AND

(b) OR

(c) NOR

(d) XOR

(e) NOT XOR

  1. (a) and (b)
  2. (b) and (c)
  3. (c), (d) and (e)
  4. (d) and (e)
in Digital Logic by Boss (30.2k points)
recategorized by | 614 views
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@mcjoshi what is linearly inseparable
+1

@Chauhan read this and this_too

XOR and XNOR are linearly inseparable.

btw It's not in GATE syllabus.

3 Answers

+3 votes

ans will be D

In Euclidean geometrylinear separability is a geometric property of a pair of sets of points. This is most easily visualized in two dimensions (the Euclidean plane) by thinking of one set of points as being colored blue and the other set of points as being colored red. These two sets are linearly separable if there exists at least one line in the plane with all of the blue points on one side of the line and all the red points on the other side. 

https://en.wikipedia.org/wiki/Linear_separability

Boolean function with 2 attributes:

01) a     ->  separable
02) b     ->  separable
03) not a    ->  separable
04) not b    ->  separable
05) a and b   ->  separable
06) a or b    ->  separable
07) a xor b   -> not separable
08) a nand b   ->  separable
09) a nor b   ->  separable
10) a xnor b   -> not separable
11) (not a) and b  ->  separable
12) a and (not b)  ->  separable
13) (not a) or b  ->  separable
14) a or (not b) ->  separable

by Boss (48.8k points)
0 votes
Find the output of all operations on the inputs 00, 01, 10, 11 and then see on the X-Y plan if they can be separated by one single straight line.

If ti is then they will be called as linearly separable otherwise not.
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