Logic Section 2.1. Symbols         and or If …, then… not.

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Presentation transcript:

Logic Section 2.1

Symbols         and or If …, then… not

p: It is Friday q: I am tired      Write each statement based upon the symbols It is Friday and I am tired It is not Friday or I am tired If I am not tired, then it is Friday

Conditionals  Hypothesis: p or the part in the statement after if  Conclusion: q or the part in the statement after then  Ex: All elephants are mammals.  Conditional: If an animal is an elephant, then it is a mammal.  Hypothesis: an animal is an elephant  Conclusion: it is a mammal p  q

Converse  Switches the hypothesis and conclusion  Ex: If you’re in a state surrounded completely by water, then you’re in Hawaii.  If you’re in Hawaii, then you’re in a state surrounded completely by water. If you live in New York, then you live in the US.  If you live in the US, then you live in New York. q  p

Inverse  Negates both the hypothesis and the conclusion  Ex: If a line has only one end point, then it is a ray.  If a line does not have only one endpoint, then it is not a ray. If I go shopping, then I will buy shoes.  If I do not go shopping, then I won’t buy shoes. ~p  ~ q

Contrapositive  Switches and negates the hypothesis and conclusion  Ex: If a shape is a square, then it is a rectangle.  If a shape is not a rectangle, then it is not a square. If you are speeding, then you will get a ticket.  If you did not get a ticket, then you were not speeding. ~q  ~ p