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PROPOSITIONAL
02 LOGIC, HARDWARE
IMPLEMENTATION,
ARITHMETIC OPERATIONS
Learning Objectives
2.1 Propositional Logic 2.2 Well-Formed Formulas and Truth Values
2.3 Connectives 2.4 Converse, Inverse and Contrapositive
2.5 Equivalence Propositional Laws 2.6 Tautology, Contradiction and Contingency
2.7 Logic Gates 2.8 Half Adder and Full Adder
Logic is the subject that deals with valid reasoning leading to inference. According to Aristotle, “logic is new and
necessary reasoning”. It is said 'new' because it lets us know the unknown and ‘necessary’ as it leads to important
conclusions. Logical reasoning is the fundamental base of some branches of Mathematics and Computer Science. Logic
may be informal, formal, symbolic or mathematical.
Symbolic logic represents logical expressions by using symbols or variables instead of using language statements.
Logical expressions are the statements that can either be true or false. An interrogative statement like “Why are plants
green?” or an imperative statement like “Do your homework” or an exclamatory statement like “What a shot!”, are
not logical statements. But a declarative statement like “Rohan is the best goalkeeper” can either be true or false or
in other words, it has a truth value. The statements that produce only true or false as answers are called propositions.
They are the building blocks of logic.
Let us examine some statements:
Statements Type
The month of May is very hot. It is a proposition as the answer can be true or false.
[mostly true]
Disha hates vegetables. It is a proposition because the answer can be yes or
no.
Good morning! It is not a proposition as commands or wishes cannot
be true or false.
What are you reading? It is not a proposition as such questions cannot be
true or false.
2.1 PROPOSITIONAL LOGIC
Propositional logic is a branch of symbolic logic that deals with propositions and how each proposition relates to
one another. It studies the ways of joining or changing propositions to form more complex propositions. A proposition
is represented by propositional variables containing a single letter generally written in lowercase.
4646 Touchpad Computer Science-XI

