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Let’s Revisit
♦ A proposition is a declarative statement that can either be true or false, but not both or any other value.
♦ Well-formed formulas (WFF) is the representation of propositional logic in the form of symbols or abbreviations.
♦ The left part (if) of a conditional is called an antecedent and the right part (then) is called a consequent.
♦ Converse is the proposition obtained by interchanging the antecedent and consequent.
♦ Inverse is the proposition obtained by taking the negated antecedent and the negated consequent in a conditional.
♦ Contrapositive is the proposition that is 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.
♦ A contingency has both 0 and 1 as its truth values.
♦ A logic gate is a digital circuit that depicts a logical relationship between the input and output voltages of the circuit. They are
the building blocks of a digital circuit.
♦ The AND gate produces 1 as output when all its inputs are 1.
♦ The OR gate produces 1 as output when any one of its inputs is 1.
♦ The NOT gate inverts the output.
♦ The NAND and NOR gates are called universal gates as they can be used to implement operations of AND, OR and NOT
gates.
♦ The XOR gate produces 1 for odd combinations of 1, and 0 in other cases.
♦ The XNOR gate produces 0 for odd combinations of 1, and 1 for even combinations of 1 or all 0’s.
♦ The half adder is a combinational circuit that is designed to perform the addition of two bits and produce the two binary
outputs as sum (S) and carry(C) bits.
♦ The full adder is a combinational circuit that is designed to perform the addition of three bits and produce the two binary
outputs as sum (S) and carry(C) bits.
MIND DRILL
Solved Questions
A. Tick ( ) the correct option:
1. Which of the following statements is a proposition?
a. Get me a glass of water.
b. May all your wishes come true!
c. What is the value of π?
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 V ∼Q V R b. P ∧ ∼Q ∧ R
c. P V Q ∧ R d. P ∨ Q ∧ ∼R
6464 Touchpad Computer Science-XI

