Introduction to mathematical reasoning Part-1 A lesson by Teja
Content . Introduction Statements Simple statements Compound statements
Introduction In mathematical language, reasoning is of two kinds - deductive and inductive. Under mathematical reasoning we'll discuss deductive kind where as inductive kind will be discussed under mathematical induction .In this lesson we'll see some fundamentals of deductive reasoning
Statements Let us start with three sentences Andhra Pradesh is a country Giraffe is taller than human being . Tomorrow is saturday When we read the first two sentences we immediately conclude that the first statement is false and the second one is true. Since there is no confusion regarding these, we call such sentences in mathematics as statements Whereas the 3rd sentence is true on friday, but not on other days So this cannot be called as a statement
Statements A statement is a sentence which is either true or false, but not both simultaneously No sentence can be called as a statement if 1) It is an exclamation Ex: a. How beautiful! b. Wow! I can't believe it! c. We're going to exhibition, Hurray!
Not a statement if 2)lt is an order or request Ex: a. Close the window b. Turn on the light 3)lt is a question Ex: a. How are you? b. Where is the golden temple? c. What's your number?
Not a statement if 4)lt involves variable time such as 'today, 'tomorrow' etc. Ex: a. Today is a sunny day b. Yesterday was a holiday c. Our anniversary is on tomorrow 5)lt involves variable places such as 'here', 'there' etc. Ex: a. You can't be safe here. b. There is a candle.
Not a statement if 6)lt involves pronouns such as he, she, they etc Ex: a. She is a doctor b. He likes chess c. They are going to a movie
Simple statements A statement is called simple if it cannot be broken down into two or more statements. Ex: a. 5 is an odd number b. A triangle has four sides c. Canberra is the capital of Australia, are simple statements
Compound statements A compound statement is made up of two or more simple . The simple statements which make a compound statement are termed as component statements. Ex: a. A square is quadrilateral and has four sides equal. ->A square is quadrilateral. A square has four sides equal. b. 24 is divisible by 6, 12 -> 24 is divisible by6 -> 24 is divisible by 12
Next lesson contents Logical connectives a. Conjunction b. Disjunction C. Negotiation d. Implications