ISC Class 12th Computer Science Chapter 1 - Boolean Algebra Important Questions with Answers

Verify if the following proposition is valid using the truth table:

(X ? Y) =>Z = (Y => Z) ? (X => Y).

According to the Principle of duality, the Boolean equation

(A+ B') • (A+ 1) =A+ B' will be equivalent to ______.

Assertion: For proposition ?A=> B, its contrapositive is B =>?A

Reason: Contrapositive is the converse of inverse for any proposition.

The complement of the Boolean expression (P' • Q) (R • S') is ______.

Write the canonical SOP expression for F (A, B) = A <=> B.

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).

Verify if the following proposition is a Tautology, Contradiction or Contingency using a truth table.

((A=>B)^?(B=>C))=>(A=>C)

Reduce the above expression X (P, S, E, B) by tiifig 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).

Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.

Reduce the Boolean function F (A,B,C,D) = ? (0, 2, 4, 6, 8, 9, 10, 11, 14) by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).

Find the complement of the following expression and reduce it by using Boolean laws.

P•( 13 ± Q)•Q•(Q+R')