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.
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.
VENN DIAGRAMS ANDCATEGORICAL PROPOSITION
1. An empty circle is used torepresent a subject class or apredicate class and is generally solabeled with an S or a P. Puttingthe name of the actual subject orpredicate class next to the circle ispreferred.
2. Shading or many parallel linesare used to indicate areas which areknown to be empty. I.e., there areno individuals existing in that area.E.g., the diagram to the rightrepresents the class of "Yeti."
3. The third symbol used is an "X"which represents "at least one" or"some" individual exists in the areain which it is placed. The diagramto the right indicates "some thing."
Venn Diagrams in General 1.Universal affirmative proposition1. The A form, "All S is P," isshown in the diagram to the right.Notice that all of the Ss are pushedout, so to speak, into the P class. IfSs exist, they must be inside the Pcircle since the left-hand lune ofthe diagram is shaded and so isempty.
2. Universal negative proposition2. The E form, "No S is P," isshown in the diagram to theright. Notice that the lens areaof the diagram is shaded and sono individual can exist in thisarea. The lens area is where Sand P are in common; hence,"No S is P." All S, if there areany, are in the left-hand lune,and all P, if there are any, arerelegated to the right-hand lune.
3. The I form, "Some S is P," ismuch more easily seen. The "X" inthe lens, as shown in the diagram tothe right, indicates at least oneindividual in the S class is also inthe P class.
4. The O form, "Some S is not P,"is also easily drawn. The S that isnot a P is marked with an "X" inthe S-lune. This area is not withinthe P circle and so is not a P. It isworth while to note, that from thisdiagram we cannot conclude that"Some S is P" because there is no"X" in the lens area. Thus, studyingthis diagram will explain why"Some S is not P" does not entail"Some S is P."
SYMBOLSSymbols comprise every language. Per se,symbols are effective tools of humanactivities whether in social interaction orin the search for knowledge.
This part will help us understand Symbolic Logic, itsbasic components and structures, symbols and fucntionsof statements constituting a basic argument.This process of proving validity is an indispensable tool torecognize the universal patters of valid arguments.
Truth-Functional Operators Four types of truth-functional compounds, 1. Conjunctions (Conjunctive Proposition)Here are some words that in many standards uses yieldconjunctions; _____and_______ Both____and________ ______but_______ ______yet_______ ______although_______ ______whereas________ ______while________
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.
2. Disjunction (Disjunctive Proposition)Here are some words that in many of their standard use yielddisjunctions.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.
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.
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.
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.