CBSE Class 11 Computer Science Question 42 of 68

Data Representation and Boolean Logic — Question 13

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Question

Question 13

State De Morgan's law and prove it with a truth table.

Answer

The first law states that when two (or more) input variables are OR'ed and negated, they are equivalent to the AND of the complements of the individual variables.

A+B\overline{A+B} = A.B\overline{A}.\overline{B}

Proof using truth table:

ABA'B'A + B(A+B)'A'.B'
0011011
0110100
1001100
1100100

The second law states that when two (or more) input variables are AND'ed and negated, they are equivalent to the OR of the complements of the individual variables.

A.B\overline{A.B} = A+B\overline{A} + \overline{B}

Proof using truth table:

ABA'B'A.B(A.B)'A' + B'
0011011
0110011
1001011
1100100