Page 19 - Computer science 868 Class 12
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1.3.4 Implication (if…then/Conditional)
Implication is represented by the symbol →. Implication results in false if the first proposition (if) is true but the second
proposition (then) is false. It returns true in all other cases. The first proposition (if) is called the antecedent and the
second proposition (then) is called the consequent.
The truth table using 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 = “25 is an integer number”.
b = “It has no decimal point”.
Then a → b = “If 25 is an integer number then it has no decimal point”.
• If x = “Computer virus is malware”.
y = “It damages data and software”.
Then x → y = “If computer virus is malware then it damages data and software”.
1.3.5 Equivalence (Biconditional)
The Equivalence connective represents the ‘if and only if’ condition. It returns true when both propositions have the
same value and false if they have different values. It is represented by the ↔ symbol.
The truth table using 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 = “19 is a prime number”.
b = “It is divisible by 1 and itself”.
Then a ↔ b = “19 is a prime number if and only if it is divisible by 1 and itself”.
• If a = “INSAT is an artificial satellite”.
b = “INSAT moves around the earth”.
Then a ↔ b = “INSAT is an artificial satellite if and only if it moves around the earth”.
Let us see some more examples.
Example 1: Consider the following simple propositions:
a = “24 is divisible by 2”
b = “24 is divisible by 3”
c = “24 is a composite number”
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Boolean Algebra 17

