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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.”
3.3.1 Precedence of the Connectives
The connectives join the simple propositions to make a compound one. There Brackets
may be multiple connectives present in a compound proposition. To analyse 1
such propositions, we must follow a certain order of evaluation of connectives, 2 Negation
which is known as the precedence of the connectives. The precedence of the Conjunction
connectives in decreasing order is listed here. 3 Disjunction
Let us understand this with the help of some examples. 4 Implication
Example 1: Consider the following simple propositions: 5 Biconditional
a = “Alok is a good batsman.” 6
b = “Alok is a good bowler.”
c = “He has won matches for his team.”
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Propositional Logic, Hardware Implementation, Arithmetic Operations 73

