Misc 2

Transcript

Misc 2 (Introduction) Contrapositive It is done by Adding not to both component statements & changing order p ⇒ q ~ q ⇒ ~ p Converse It is done by changing order of statement p ⇒ q Then q ⇒ p State the converse and contrapositive of each of the following statements: (i) p: A positive integer is prime only if it has no divisors other than 1 and itself. This statement is not in if-then form Writing in if-then form The statement can written as “If A positive integer is prime , then it has no divisor other than 1 itself” Converse If positive integer has no divisor other than 1 and itself , then it is prime Contrapositive It a positive integer has divisor other than 1 and itself , then it is not prime Misc 2 State the converse and contrapositive of each of the following statements: (ii) q: I go to a beach whenever it is a sunny day. The above statement can be written as “If it is a sunny day, then I go to a beach” Converse If I go to a beach, then it is a sunny day Contrapositive If I do not go to a beach, then it is not a sunny day Misc 2 State the converse and contrapositive of each of the following statements: (iii) r: If it is hot outside, then you feel thirsty. If It is a hot outside then you feel thirsty Converse It you feel thirsty, then it is hot outside. Contrapositive If you do not feel thirsty , the it is not hot outside.