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Definition
A truth table is a table which shows the truth values of all the possible combinations of inputs. It is used to find if a
compound statement is true or false.
3.3 CONNECTIVES
Now, we know that connectives or logical operators join two or more simple propositions to form a compound
proposition. There are mainly five connectives which are as follows:
• Negation (NOT): It inverts a single statement. It is also called a unary connective. If a proposition is true, negation
makes it false and vice versa. Negation is represented by ˜(tilde) or ‘ (apostrophe) or ̅ (bar).
The truth table for negation is given below considering ‘a’ as a propositional variable:
a ∼a
0 1
1 0
If a = “It is raining heavily” then ∼a = “It is not raining heavily.”
If b = “Planet X is the ninth planet” then ∼b = “Planet X is not the ninth planet.”
• Conjunction (AND): It is a binary connective as it joins two or more simple propositions. It results in true if all
propositional variables are true. If any variable is false, the resulting output is false. A conjunction is represented by
a dot (.) or (∧). The truth table for conjunction using two variables ‘a’ and ‘b’ is given below:
a b a ∧ b
0 0 0
0 1 0
1 0 0
1 1 1
If a = “10 is an even number.”
b = “10 is divisible by 5.”
Then, a ∧ b = “10 is an even number and 10 is divisible by 5.”
If x = “Light is a form of energy.”
y = “Light travels in a straight line.”
Then, x ∧ y = “Light is a form of energy and light travels in a straight line.”
• Disjunction (OR): It is also a binary connective that results in true if any one proposition is true. The output is false
only when both propositions are false. A disjunction is represented by a plus (+) or (∨).
The truth table for disjunction using two variables ‘a’ and ‘b’ is given below:
a b a ∨ b
0 0 0
0 1 1
1 0 1
1 1 1
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.”
7272 Touchpad Computer Science-XI

