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To be recruited as the Principal in a renowned College, a candidate must satisfy any one of the…
To be recruited as the Principal in a renowned College, a candidate must satisfy any one of the following criteria:
• The candidate must be a Postgraduate and should either possess a B.Ed. degree or a teaching experience of more than 15 years.
OR
• The candidate must be an employee of the same college with a teaching experience of more than 15 years.
OR
• The candidate must be a Postgraduate but not an employee of the same college and should have a teaching experience of more than 15 years.
The inputs are:
(In all the above cases, 1 indicates yes and 0 indicates no)
Output: X - Denotes eligibility of a candidate [1 indicates eligibility and 0 indicates ineligibility in all cases]
Draw the truth table for the inputs and outputs given above and write the SOP expression for X (P, S, E, B).
| INPUTS | |
| P | Candidate is a Postgraduate |
| S | Candidate is an employee of the same College |
| E | Candidate has a teaching experience of more than 15 years |
| B | Candidate possesses a B.Ed. degree |
Answer
Answer
AICondition 1 (Postgraduate & (B.Ed OR Exp>15)): P.(B+E)
Condition 2 (employee with Exp>15): S.E
Condition 3 (Postgraduate, not employee, Exp>15): P.S'.E
X(P,S,E,B) = P.(B+E) + S.E + P.S'.E
Truth table:
X(P,S,E,B) = Σ(6,7,9,10,11,13,14,15)
Canonical SOP:
X(P,S,E,B) = P'SEB' + P'SEB + PS'E'B + PS'EB' + PS'EB + PSE'B + PSEB' + PSEB
| P | S | E | B | X |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |
From ISC 2024 Computer Science Paper 1, question 3(i).