Page 20 - Computer science 868 Class 12
P. 20
Convert the following symbolic expressions into meaningful statements:
i. (a ∨ b) → c
ii. ∼a ↔ ∼c
iii. c → (a ∨ b)
iv. a ∧ b
v. ∼(a ∨ b)
Solution:
i. If 24 is divisible by 2 or 24 is divisible by 3 then 24 is a composite number.
ii. 24 is not divisible by 2 if and only if 24 is not a composite number.
iii. If 24 is a composite number, then 24 is divisible by 2 or 24 is divisible by 3.
iv. 24 is divisible by 2 and 24 is divisible by 3.
v. It is not true that 24 is divisible by 2 or 24 is divisible by 3.
Example 2: Consider the following propositions:
x = “Basic is a programming language”
y = “Basic is a beginner’s language”
z = “Basic is simple and easy to learn”
Write the following statements in symbolic form:
i. If Basic is simple and easy to learn then Basic is a beginner’s language.
ii. Basic is a programming language or Basic is a beginner’s language if and only if it is simple and easy to learn.
iii. Basic is a programming language and Basic is a beginner’s language and Basic is simple and easy to learn.
Solution:
i. z → y
ii. (x ∨ y) ↔ z
iii. x ∧ y ∧ z
1.4 WELL-FORMED FORMULAS, PREMISES AND SYLLOGISM
Well-formed formula abbreviated as WFF is a propositional form that follows the rules given below:
• A proposition or a variable representing a proposition is WFF.
• Each atomic formula is a WFF.
• If A and B are two WFFs then ∼A, ∼B, (A ∧ B), (A ∨ B), (A → B), (A ↔ B) are all WFFs.
A Premise is a conditional statement used to establish a conclusion. The logical process of deriving a conclusion from
a given proposition is called Syllogism.
1.5 CONVERSE, INVERSE AND CONTRAPOSITIVE
We know that a conditional proposition a → b means if a then b. In this proposition, the first part is called the antecedent
or premise and the second part is called the consequent or conclusion. If we interchange antecedent and consequent
or complement antecedent and consequent, then we get a separate set of conditionals. The three different cases that
may arise are:
• Converse: The converse of a conditional is obtained by interchanging the antecedent with the consequent of that
conditional.
For any conditional a → b, its converse will be b → a.
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