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Fallacy

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2. Here is the translation of the statements found in examples 13-16, and 18 to their corresponding symbolic expressions:
Example #12: If Spot ran away, then the gate was left open.
Let’s assume: S = Spot ran away. T = The gate was left open. → = IF-THEN Therefore, Symbolic expressions: S → T
Antecedent = Spot ran away
Consequent = The gate was left open. Example #13: I will never talk to you again if you don’t apologize
Let’s assume: Y = You apologize. I = I will talk to you again. → = IF-THEN ~ = NOT Therefore, Symbolic expressions: ~Y→ ~ I
Antecedent = You don’t apologize.
Consequent = I will never talk to you again
Example #14: Bring me an ice-cream cone and I will be happy
Let’s assume: I = Bring me an ice-cream cone H = I will be happy. & = AND Therefore, Symbolic expression is I & H.
Antecedent = You bring me an ice cream.
Consequent = I will be happy.

Example #15: Loving someone means you never throw dishes at them.
Let’s assume: L = You love someone. D = You throw dish at them. → = IF-THEN ~ = NOT Therefore, Symbolic expressions: L→ ~ D
Antecedent = You love someone. Consequent = You never throw dishes at them.

Example #16: If Dick goes to the basketball game, then either he got free ticket or he borrowed money for one.
Let’s assume: B = Dick goes to the basketball game F = He got free ticket H = He borrowed money for one. V = OR → = IF-THEN Therefore, Symbolic expressions: B → (F v H)
Antecedent = Dick goes to the basketball game. Consequent = He got free ticket, or He borrowed money for one.

3. Here are the valid arguments with general form and examples:
A. Modus Ponens
General Form
1) If p, then q.
2) p.
-------------------
3) Thus, q.
Examples
1) If I pass the exam, then I am happy.
2) I pass the exam.
--------------------------------------------
3) Thus, I am happy.
Symbolic Expression
1) P → H.
2) P.
---------------
3) Thus, H. B. Modus Tollens
General Form
1) If p, then q.
2) Not q.
-------------------
3) Thus, not p.
Examples
1) If I study, then I get good grades.
2) I dIdn’t get good grades.
--------------------------------------------
3) Thus, I’m not happy.
Symbolic Expression
1) S → G.
2) ~G.
---------------
3) Thus, ~H.
C. Hypothetical Syllogism
General Form
1) If p, then q.
2) If q, then r.
-------------------
3) Thus, if p then r.
Examples
1) If I study, then I get good grades.
2) If I get good grade, then I pass the course.
--------------------------------------------
3) Thus, if I study, then I pass the course.
Symbolic Expression
1) S → G.
2) G → C
---------------
3) Thus, S → C
D. Disjunctive Syllogism
General Form
1) p, or q.
2) Not p.
-------------------
3) Thus, q.
Example
1) I study or I get good grades.
2) It is not the case that I didn’t study.
--------------------------------------------------------
3) Thus, I get good grades.
Symbolic Expression
1) S v G.
2) ~S
---------------
3) Thus, G
E. Dilemma
General Form
1) p or q.
2) If p, then r.
3) If q, then s.
-------------------
4) Thus, r or s.
Example
1) I study or I get good grades.
2) If I study, then I pass the course.
3) If I get good grades, then I learned the material.
---------------------------------------------------------------
4) Thus, I pass the course or I learned the material.
Symbolic Expression 1) S v G.
2) S → C.
3) G → M.
-------------------
4) Thus, C v M

4. The advantage of translating verbal arguments to symbolic argument forms are as follows: * Consumes less amount of time to understand the meaning of sentence. * Avoids double meaning senses. * Easy to recognize whether particular argument is deductive or inductive. * Translation of verbal arguments to a symbolic argument helps one to examine the structure of the declarative sentence (analysis) to reveal logical connections. * And, recognizing logical connections may clarify meaning in reading, writing, and mathematics. * Translation of verbal arguments to symbolic argument helps one to examine the structure of an statements in detail (analysis). * Symbolizing this structure can show how premises and a conclusion are related in valid, or invalid, argument forms (evaluation).

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