Page 46 - Computer science 868 Class 12
P. 46
Let’s Revisit
♦ Proposition is a declarative statement that can either be true or false, but not both or any other value.
♦ The different connectives used in propositional logic are negation, conjunction, disjunction, conditional and bi-conditional.
♦ The left part (if) of a conditional is called antecedent and the right part (then) is called the consequent.
♦ Converse is the proposition obtained by interchanging antecedent and consequent, while the inverse is the proposition
obtained by taking negated antecedent and negated consequent. On the other hand, the contrapositive is the proposition
that is the inverse of its converse.
♦ A tautology is a proposition that has 1 as its truth value, and a contradiction has 0 as its truth value. Contingencies have
both 0 and 1 as their truth value.
♦ Boolean algebra has laws that help in simplifying a complex Boolean expression which further reduces the number of
digital gates required to represent a circuit. Some important laws are Complement law, Idempotent law, Involution law,
Distributive law, Associative law and De Morgan’s law.
♦ Each Boolean law has its dual with can be obtained by interchanging OR with AND or 0 with 1.
♦ A truth table is a mathematical table that lists the output of any Boolean expression for all the possible combinations of its
inputs.
♦ A minterm can be defined as the product terms of all the variables present in the expression both in complemented and
normal forms.
♦ A maxterm can be defined as the sum terms of all the variables present in the expression both in complemented and un
complemented forms.
♦ Any Boolean expression can either be the sum of its minterms or Sum of Products abbreviated as SOP or the product of its
maxterms or Product of Sum abbreviated as POS.
♦ The K-map method is a graphical method of simplifying a Boolean expression. In this method, a rectangle or a square grid
of 2n (where n represents the number of Boolean variables that constitute the expression) is drawn in a definite pattern.
MIND DRILL
Solved Questions
A. Tick ( ) the correct option:
1. Which of the following statements is a proposition?
a. Go board the bus. b. May God bless you!
c. What is the value of g? d. The only odd prime number is 2.
2. Let, P: He is honest., Q: He is dedicated., R: He is hardworking. Then “He is honest or dedicated and not hardworking.” is best
represented by?
a. ∼P ∨ ∼Q ∨ R b. P ∧ ∼Q ∧ R
c. P ∨ Q ∧ R d. P ∨ Q ∧ ∼R
3. Let, P: I live in Kolkata, Q: I love sweets, then q' → p is?
a. If I live in Kolkata then I love sweets. b. If I do not live in Kolkata then I do not love sweets.
c. If I do not love sweets then I live in Kolkata. d. If I love sweets then I live in Kolkata.
4. A+1 = 1 is a
a. Tautology b. Contradiction
c. Contingency d. Converse
5. Contrapositive of a conditional a' → b' is
a. a → b b. b → a
c. b' → a' d. a' ∨ b'
4444 Touchpad Computer Science-XII

