Venndiag
Download as ppt, pdf0 likes377 views
1. Venn diagrams use circles and areas to represent categorical propositions about relationships between classes. 2. Universal affirmative propositions are represented by one class being fully contained within the other. Universal negative propositions use a shaded area to show no overlap between classes. 3. Symbolic logic uses symbols and operators like conjunction, disjunction, implication, equivalence and negation to construct statements and analyze arguments for validity.
Venndiag
- 1. VENN DIAGRAMS AND CATEGORICAL PROPOSITION
- 2. 1. An empty circle is used to represent a subject class or a predicate class and is generally so labeled with an S or a P. Putting the name of the actual subject or predicate class next to the circle is preferred.
- 3. 2. Shading or many parallel lines are used to indicate areas which are known to be empty. I.e., there are no individuals existing in that area. E.g., the diagram to the right represents the class of "Yeti."
- 4. 3. The third symbol used is an "X" which represents "at least one" or "some" individual exists in the area in which it is placed. The diagram to the right indicates "some thing."
- 5. Venn Diagrams in General 1.Universal affirmative proposition 1. The A form, "All S is P," is shown in the diagram to the right. Notice that all of the S's are pushed out, so to speak, into the P class. If S's exist, they must be inside the P circle since the left-hand lune of the diagram is shaded and so is empty.
- 6. 2. Universal negative proposition 2. The E form, "No S is P," is shown in the diagram to the right. Notice that the lens area of the diagram is shaded and so no individual can exist in this area. The lens area is where S and P are in common; hence, "No S is P." All S, if there are any, are in the left-hand lune, and all P, if there are any, are relegated to the right-hand lune.
- 7. 3. The I form, "Some S is P," is much more easily seen. The "X" in the lens, as shown in the diagram to the right, indicates at least one individual in the S class is also in the P class.
- 8. 4. The O form, "Some S is not P," is also easily drawn. The S that is not a P is marked with an "X" in the S-lune. This area is not within the P circle and so is not a P. It is worth while to note, that from this diagram we cannot conclude that "Some S is P" because there is no "X" in the lens area. Thus, studying this diagram will explain why "Some S is not P" does not entail "Some S is P."
- 10. SYMBOLS Symbols comprise every language. Per se, symbols are effective tools of human activities whether in social interaction or in the search for knowledge.
- 11. This part will help us understand Symbolic Logic, its basic components and structures, symbols and fucntions of statements constituting a basic argument. This process of proving validity is an indispensable tool to recognize the universal patters of valid arguments.
- 12. Truth-Functional Operators Four types of truth-functional compounds, 1. Conjunctions (Conjunctive Proposition) Here are some words that in many standards uses yield conjunctions; _____and_______ Both____and________ ______but_______ ______yet_______ ______although_______ ______whereas________ ______while________
- 13. Manuel is strong and Gina is pretty. Both Manuel is strong and Gina is pretty. Manuel is strong but Gina is pretty. Manuel is strong yet Gina is pretty. Manuel is strong although Gina is pretty. Manuel is strong whereas Gina is pretty. Manuel is strong while Gina is pretty.
- 14. 2. Disjunction (Disjunctive Proposition) Here are some words that in many of their standard use yield disjunctions. Either_____or_______ ______or_______ ______unless_______ Either Manuel is strong or Gina is pretty. Manuel is strong or Gina is pretty. Manuel is strong unless Gina is pretty.
- 15. 3. Implication (Conditional Proposition) If ____then______ If____, _____ _____only if_____ _____if______ _____provided that______ not____unless_______ If Manuel is strong then Gina is pretty. If Manuel is strong, Gina is pretty. Manuel is strong only if Gina is pretty. Gina is pretty if Manuel is strong. Gina is pretty provided that Manuel is strong. Manuel is not strong unless Gina is pretty.
- 16. 4. Material Equivalence (Bi-Conditional Proposition) Here are some phrases that in many of their standard uses yield material equialence: _______if, and only if,_______ _______when, and only when,______ _______is equivalent to _______ These phrases can result into material equivalences, such as: Manuel is strong if, and only if, Gina is pretty. Manuel is strong when, and only when Gina is pretty. Manuel is strong is equivalent to Gina is pretty.
- 17. Negation (Contradictory or denial) It is not the case that______ It is not true that_______ There is no way that________ ______is false. It is false that_______ It is not the case that Manuel is strong. It is not true that Manuel is strong. There is no way that Manuel is strong. ¡°Manuel is strong¡± is false. It is false that Manuel is strong.
- 18. End
Editor's Notes
- #16: Based on these, we can make truth-functional compounds that expresses that the first sentence unit is a logical condition of the second. The first part is called the antecedent of the implication and the second part is the consequent of the implication. It asserts the relationships.
- #18: There is another device, (though not used to form compound sentences) that is very common in almost all natural languages. The device operates to convert the truth-value of a given sentence unit and compound sentences. We refer to this operation as negation. That sentence units can be negated, or asserted not to be true, by using words or phares such as.