HSC Science (Computer Science) 12th Board ExamMaharashtra State Board
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# Solution for Construct the Simplified Circuit for the Following Circuit - HSC Science (Computer Science) 12th Board Exam - Mathematics and Statistics

ConceptMathematical Logic Application - Introduction to Switching Circuits

#### Question

Construct the simplified circuit for the following circuit:

#### Solution

Let p : switch S1 is closed
q : switch S2 is closed
r : switch S3 is closed
~ p : switch S1 is open
~ q : switch S2 is open
~ r : switch S3 is open
The symbolic form of the given circuit
[p ∧ (q ∨ r)] ∨ [~ r ∧ ~ q ∧ p]
= p ∧ [(q ∨ r) ∨ (~ q ∧ ~ r) ….(Distributive law)
= p ∧ [(q ∨ r) ∨ ~ (q  r)] ….(De Morgan’s law)
= p ∧ T ….(Compliment law)
= p ….(Identity law)
The new simplified circuit is

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (October) (with solutions)
Question 3.1.1 | 3.00 marks
Solution Construct the Simplified Circuit for the Following Circuit Concept: Mathematical Logic - Application - Introduction to Switching Circuits.
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