Question 32 (i) - Sample Paper 2 by Teachoo - Teachoo Sample Paper

Simplify the following Boolean expression using De Morgan's laws and draw the truth table of the simplified expression:

not (A or B) and not (A and B)

Answer:

Answer by student

The simplified expression is:

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not A and not B

The truth table is:

Detailed answer by teachoo

To simplify the expression, we can use De Morgan’s laws, which state that:

• not (A or B) = not A and not B

• not (A and B) = not A or not B

Applying these laws, we get:

not (A or B) and not (A and B) = (not A and not B) and (not A or not B)

Using the distributive property of and, we get:

(not A and not B) and (not A or not B) = (not A and not B and not A) or (not A and not B and not B)

Using the idempotent property of and, we get:

(not A and not B and not A) or (not A and not B and not B) = (not A and not B) or (not A and not B)

Using the idempotent property of or, we get:

(not A and not B) or (not A and not B) = not A and not B

Hence, the simplified expression is:

not A and not B

To draw the truth table, we need to list all the possible combinations of values for A and B, which are 0 (False) or 1 (True). Then, we need to evaluate the original expression and the simplified expression for each combination. 

The truth table is shown below:

We can see that the original expression and the simplified expression have the same output for every input, which means they are equivalent.

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