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Let us understand this with the help of some examples.
Example 1: Consider the following simple propositions:
a = “Alok is a good batsman.”
b = “Alok is a good bowler.”
c = “He has won matches for his team.”
Convert the following symbolic expressions into meaningful statements:
a. (a ∨ b) ∧ c b. ∼a ∧ ∼c c. a → c d. b ↔ c e. a → ∼b
Answer: a. Alok is a good batsman or Alok is a good bowler and he has won matches for his team.
b. Alok is not a good batsman and he has not won matches for his team.
c. If Alok is a good batsman, then he has won matches for his team.
d. Alok is a good bowler if and only if he has won matches for his team.
e. If Alok is a good batsman then he is not a good bowler.
Example 2: Consider the following simple propositions:
x = “Java is a programming language.”
y = “Java is used in web development.”
z = “Java is simple and easy to learn.”
Write the following statements in symbolic form:
a. Java is a programming language and it is not simple and easy to learn.
b. If Java is a programming language or it is simple and easy to learn then it is used in web development.
c. Java is a programming language if and only if Java is used in web development.
d. Java is simple and easy to learn or Java is a programming language and it is used in web development.
Answer: a. x ∧ ∼z b. (x ∨ z) → y c. x ↔ y d. z ∨ (x ∧ y)

3.4 CONVERSE, INVERSE AND CONTRAPOSITIVE
A conditional proposition a → b means if a then b. Here, the first part is called antecedent or premise and the second
part is called consequent or conclusion. If we interchange antecedent and consequent or complement antecedent and
consequent, then we get a separate set of conditionals. Three different cases may arise which are as follows:
• Converse: The converse of a conditional is obtained by interchanging antecedent with the consequent of that
conditional.
For any conditional a → b, its converse will be b → a.
• Inverse: The inverse of a conditional is obtained by complementing the antecedent and consequent of that
conditional.
For any conditional a → b, its inverse will be a' → b'.
• Contrapositive: The contrapositive of a conditional is obtained by interchanging the complemented antecedent
with the complemented consequent of that conditional. It is equivalent to the converse of the inverse of that
conditional.
For any conditional a → b, its contrapositive will be b' → a'.
Example: Consider the following propositions:
p = “232 is equal to its reverse.”

q = “It is a palindrome.”
Write the a. converse b. inverse c. contrapositive of the conditional p → q.
Answer: Conditional p → q = “If 232 is equal to its reverse then it is a palindrome.”
a. Converse q → p = “If it is a palindrome then 232 is equal to its reverse.”
b. Inverse p' → q' = “If 232 is not equal to its reverse then it is not a palindrome.”
c. Contrapositive q' → p' = “If it is not a palindrome then 232 is not equal to its reverse.”

Propositional Logic, Hardware Implementation, Arithmetic Operations 71