CLASS-XI COMPUTER SCIENCE CHAPTER-3 ASSIGNMENT SOLUTION

1. Verify using truth table that X + XY = X for each X, Y in {0,1}

2. Verify using truth table that \( \overline{(X + Y)} \) = \( \overline{X}\overline{Y}\) for each X, Y in {0,1}

3. Give truth table for the Boolean expression: \( \overline{(X+\overline{Y})} \).

4.  Draw truth table for the following equations:
(a) M = N (P+R)

(b) M = N+P+NP̄

5. Using truth table, prove that: AB+BC+C= AB+CĀ

6. State the principal of duality in boolean algebra and give the dual of the boolean expression.

(X+Y).( X’+Z’).(Y+Z)

According to the principle of duality, a true boolean statement or expression can be converted to its dual form by replacing the “0”s in the statement or expression with “1”s, and vice versa and by replacing the “+”s in the statement or expression with “.”s, and vice versa.

The dual form of (X+Y)(X’+Z’ ).(Y + Z)  is (X.Y)+(X’.Z’ )+(Y.Z)

In the above dual expression all the “+”s were replaced by “.”s, and vice versa.

7. Prove the idempotence law of boolean algebra with the help of a truth table

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