Logic
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Transcript of Logic
LogicInductive Reasoning – a process of reasoning that a rule or statement is true because of a specific case (drawn from a pattern)1. Look for a pattern2. Make a conjecture3. Prove or find a counterexample
To disprove need a counterexample (a drawing, statement or number)
• Deductive Reasoning – Process of using logic to draw conclusions using definitions, facts, or properties. ( postulates and Theorems are facts)
Examples Conjecture1. 1, 2, 4, 7, 11, _____
2. Jan, March, May, ______
• Complete- The sum of 2 positive integers is ___________
Prove or find a counterexampleFor all integers n, is positive.
2 complementary angles can not be
3n
Conditional If p, then q p is hypothesis q is conclusion
p→q
Converse If q, then p flip
q→pInverse If not p, then not q negate
~p→~qContrapositive If not q, then not p flip & negate
~q→~p
Truth value is true in all situations except when hypothesis is true and the conclusion is false. p = If you make an A q = I will buy you a car
p → q T T T You made an A, then I bought the car.
T F F You made an A, but I did not buy the car.
F T T You did not make an A, but I bought the car anyway.
F T F You did not make an A, then I did not buy the car.
Counterexample :Make the if true and the then false.
Write the converse, inverse, and contrapositive of the following. State if true or false. If false give counterexample.
If m<A = 30, then <A is acute.
If m<A = 30, then <A is acute. p → q
Converse q → p If <A is acute, then m<A = 30.
Inverse ~p → ~qIf m<A ≠30, then <A is not acute.
Contrapositive ~q → ~pIf <A is not acute, then m<A ≠ 30.
Write the converse, inverse, and contrapositive of the following. State if true or false. If false give counterexample.
If 2 angles are vertical, then they are
If 2 angles are vertical, then they are p → q
Converse q → p If 2 angles are , then they are vertical.
Inverse ~p → ~qIf 2 angles are not vertical, then they are not
Contrapositive ~q → ~pIf 2 angles are not , then they are not vertical.
Biconditional
p if and only if qp↔q
All definitions are biconditional.Two angles are supplementary if and only if their
sum is 180°.