Basic of Discrete Mathematics – Propositions
What is Propositions?
A Proposition is a declarative sentence that is true or false but not both.
A proposition must be declarative sentence otherwise, we can’t say this proposition.
Example: “Now I am reading a blog.” is a proposition but “He is a good boy.” isn’t a proposition. Because, In first sentence it has been declared subject (I) but in next sentence, it hasn’t been declared that who is ‘he’. For that, subject has been hidden from actual informative person and it isn’t declarative sentence. According to definition of proposition, we can’t say the second sentence as a proposition.
Above the sentence is an example of proposition that give us information with the return value ‘True’ or ‘False’.
Similarly, the following sentences are also proposition:
1. “Every student in your class has taken ‘Calculus’ or ‘Discrete Mathematics’.”
2. “Today is Friday and it is rainy day.”
3. 5 + 6 = 11
What is Propositional Variables?
Propositional Variable is such type variable that represent propositions by using letters.
Example, we can represent “Dhaka is the capital of Bangladesh” proposition by using P and “I live in Dhaka City” by using Q etc.
What is Compound Proposition?
A new formed proposition from existing propositions by using logical operator is called Compound Proposition.
If we want to add the above two propositional variable P and Q by using Conjunction Operator (∧), then it will be P∧Q and the compound proposition will be “Dhaka is the capital of Bangladesh and I live in Dhaka City.”