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Section 1.3 in the book.
Propositional Equivalences
Learning Goals
- Know the definition of tautology, contradiction, contingency, and logical
equivalence.
- Be familiar with the basic laws of logical equivalence.
- Use laws of logical equivalence (also known as algebraic laws of logic) to simplify
compound propositions and identify them as tautologies, contradictions or
contingencies or to prove logical equivalences.
Homework
Read Module 1: Slides and Examples.
Complete: Edfinity Propositional Equivalences
Written Homework Propositional Logic
WebWork: work on assignment 10.
Section 1.3 in the book.
Converse, inverse, contrapositive of a conditional statement ๐ โ ๐.
Conditional: ๐ โ ๐ ; Converse: ๐ โ ๐;
Inverse: ยฌ๐ โ ยฌ๐ ; Contrapositive : ยฌ๐ โ ยฌ๐;
If I study, then I get an A on my exam.
Converse:
Inverse:
Contrapositive:
Tautology : A logical expression which is always true regardless of the truth values
of the variables.
Contradiction : A logical expression which is always false regardless of the truth
values of the variables.
Neither tautology nor contradiction is called a contingency.
Section 1.3 in the book.
3. Laws of D Morgan, the negation of disjunction and conjunction
๐: Joe is famous ๐: Joe is rich
4. Negation of conditional: ยฌ
Section 1.3 in the book.
Statement
If x is a rational number and y is a rational number, then x+y is a rational number.
Find the negation of the statement:
Find the contrapositive of the statement:
Section 1.3 in the book.
Example : Select the statement that is logically equivalent to
โIf you can dream it, then you can achieve itโ.
๐ โ โyou can dream itโ and ๐ โ โyou can achieve itโ
Express each of the following conditional, in โIf โฆthenโ and then use the variable ๐
and ๐ express the implication.
a. You canโt achieve it unless you dream it.
b. You can achieve it only if you dream it.
c. Achieving it is a sufficient condition for dreaming it.
d. Dreaming it is a necessary condition for achieving it.
e. Achieving it is a necessary condition for dreaming it.
