Logic Terminology Statement- declarative sentence that is either true or false Opinion- a belief about matters commonly considered to be subjective,

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Presentation transcript:

Logic Terminology

Statement- declarative sentence that is either true or false Opinion- a belief about matters commonly considered to be subjective, i.e., it is based on that which is less than absolutely certain

Law of Excluded Middle: Any statement is either true or false Law of Contradiction: A statement cannot be both true and false

Deduction- when you reason from accepted statements to a conclusion or new fact, you are using deductive reasoning. If you make an A on your Geometry test, I will give you $5.00.

Suppose p is “2 + 5 = 12”. Remember a statement can be true or false. Suppose I wanted to write does not equal 12. I would need the negation of p. Suppose p is “it is sunny” The negation of p is “it is not sunny” Here is the way to denote negation: ~p. So any time you see ~p, what does it mean? Negation- the denial of the statement

If p is true what can we say about ∼ p? ∼ p is false! Can ∼ p ever be true? Only if p is false!

Disjunctions p: I buy you new jeans q: I buy you new shoes Your mom might say, “Lets go shopping. I’ll buy your new jeans OR I’ll buy you new shoes. Disjunctions- a compound statement formed by joining two statements with the connector ‘OR’ p v q “p or q”

Conjunctions Let’s go shopping. I’ll buy you new jeans AND I’ll buy you new shoes. Conjunctions- a compound statement formed by joining two statements with the connector AND. p ʌ q “p and q”

pL88 pL88

Conditional Statement Implications: if… then statement (also called the conditional statement) ‘if statement’ is the hypothesis, ‘then statement’ is the conclusion If Johnny exercises, then he will lose weight.

Symbols

Lets Practice! What is the conclusion of the following statement? All people who graduate high school get a job. Jessica graduates high school. Jessica gets a job!

Given p: I am an honors student. q: I play football. 1. ∼ p I am not an honors student. 2. p ʌ ∼ q I am an honors student and I do not play football. 3. ∼ (p v q) ∼ (I am an honors student or I play football.) I am not an honors student and I do not play football.

Translate the following into symbolic logic: 1. I do not play football. ∼ q 2. I am not an honors student and I play football. ∼ p ʌ q 3. I am an honors student or I play football. p v q