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A training institute intends to give scholarships to its students as per the criteria given below :

The student has excellent academic record but is financially weak.

OR

The student does not have an excellent academic record and belongs to a backward class.

OR

The student does not have an excellent academic record and is physically impaired.

The inputs are :

INPUTS
A Has excellent academic record 
F Financially sound
C Belongs to a backward class
I Is physically impaired  

(In all the above cases 1 indicates yes and 0 indicates no).

Output : X [1 indicates yes, 0 indicates no for all cases]

Draw the truth table for the inputs and outputs given above and write the SOP expression for X (A,F, C,I).

1 Answer

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Best answer

From the question, we have four inputs A, F, C, I and on output X. The truth table for given variables is shown.

A F C I X
0 0 0 0 0
0 0 0 1 1
0 0 1 0 1
0 0 1 1 1
0 1 0 0 0
0 1 0 1 1
0 1 1 0 1
0 1 1 1 1
1 0 0 0 0
1 0 0 1 0
1 0 1 0 0
1 0 1 1 0
1 1 0 0 1
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1

So, the SOP expression is

A' F' C' I + A' F' C I' + A' F' CI + A' FC' I + A' FC I' + A' FCI + AFC' I' + AFC' I + AFC I' + AFCI

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