ISC (Commerce) Class 12 - CISCE Important Questions for Computer Science (Theory)

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) = π (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')

How is a decoder different from a multiplexer?

Write the cardinal form of the maxterm X + Y' + Z.

The compliment of the Boolean expression Aꞌ • (B • Cꞌ + Bꞌ • C).

According to the Principle of duality, the Boolean equation (Aꞌ + B) • (1 + B) = Aꞌ + B will be equivalent to ______.

Distributive law states that ______.

The complement of the reduced expression of F(A,B) = ∑ (0,1,2,3) is ______.

Study the given propositions and the statements marked Assertion and Reason that follow it. Choose the correct option on the basis of your analysis.

p = I am a triangle

q = I am a three-sided polygon

s1 = p → q

s2 = q → p

Assertion: s2 is converse of s1

Reason: Three-sided polygon must be a triangle.

A shopping mall announces a special discount on all its products as a festival offer only to those who satisfy any one of the following conditions.

• If he/she is an employee of the mall and has a service of more than 10 years.
                                   OR
• A regular customer of the mall whose age is less than 65 years and should not be an employee of the mall.
                                   OR
• If he/she is a senior citizen but not a regular customer of the mall.

The inputs are:

(In all the above cases, 1 indicates yes and 0 indicates no.)

Output: X - Denotes eligible for discount [1 indicates YES and 0 indicates NO in all cases]

Draw the truth table for the inputs and outputs given above and write the SOP expression for X ( E, R, S, C ).

Reduce the above expression X ( E, R, S, C ) by using 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(P,Q,R,S) = (P+Q+R+S) • (P+Q+R+Sꞌ) • (P+Q+Rꞌ+S) • (P+Qꞌ+R+S) • (P+Qꞌ+R+Sꞌ) • (P+Qꞌ+Rꞌ+S) • (P+Qꞌ+Rꞌ+Sꞌ) •(Pꞌ+Q+R+S) • (Pꞌ+Q+R+Sꞌ) by using 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs).

From the given logic diagram:

1. Derive Boolean expression and draw the truth table for the derived expression
2. If A=1, B=0 and C=1, then find the value of X.