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 If a = “Raj is wearing a blue jersey.”
b = “Raj is wearing a red jersey.”
Then a ∨ b = “Raj is wearing a blue jersey or Raj is wearing a red jersey.”
 If m = “Rina is a banker.”
n = “Rina is a lawyer.”
Then m ∨ n = “Rina is a banker or Rina is a lawyer.”
• Implication (if..then/Conditional): It is represented by the symbol ‘→’. It implies results is false if the first proposition
(if) is true but the second one (then) is false. It is true in all other cases. The first proposition is called the antecedent
and the second proposition is called the consequent.
The truth table for conditional using two variables ‘a’ and ‘b’ is as follows:
a b a → b
0 0 1
0 1 1
1 0 0
1 1 1
 If a = “17 is divisible only by 1 and 17.”
b = “17 is a prime number.”
Then a → b = “If 17 is divisible only by 1 and 17 then 17 is a prime number.”
 If x = “I like coding.”
y = “I like Java.”
Then a → b = “If I like coding then I like Java.”
• Equivalence (Biconditional): It is also referred to as if and only if. It is true when both propositions have the same
value and false if they have different values. It is represented by ↔ symbol.
The truth table for biconditional using two variables ‘a’ and ‘b’ is given below:
a b a ↔ b
0 0 1
0 1 0
1 0 0
1 1 1
 If a = “8 is an even number.”
b = “8 is divisible by 2.”
Then a ↔ b = “8 is an even number if and only if it is divisible by 2.”
 If a = “Moon is a satellite.”
b = “Moon moves around the earth.”
Then a ↔ b = “Moon is a satellite if and only if it moves around the earth.”

Brackets
3.3.1 Precedence of the Connectives 1 Negation
The connectives join the simple propositions to make a compound one. There 2
may be multiple connectives present in a compound proposition. To analyse 3 Conjunction
such propositions, we must follow a certain order of evaluation of connectives, Disjunction
which is known as the precedence of the connectives. The precedence of the 4
connectives in decreasing order is listed here. 5 Implication

6 Biconditional

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