translate the argument into symbolic form. then determine whether the argument is valid or invalid. you may use a truth table or, if applicable, compare the arguments symbolic form to a standard valid or invalid form.

the bug is dead or the bird is white.
the bug is not dead.
therefore, the bird is not white.

let p represent he bug is dead,\ and let q represent he bird is white.\

is the argument valid or invalid?
a. valid
b. invalid

Question

translate the argument into symbolic form. then determine whether the argument is valid or invalid. you may use a truth table or, if applicable, compare the arguments symbolic form to a standard valid or invalid form.

the bug is dead or the bird is white.
the bug is not dead.
therefore, the bird is not white.

let p represent 	he bug is dead,\ and let q represent 	he bird is white.\

is the argument valid or invalid?
a. valid
b. invalid

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Disjunctive Syllogism", "Fallacy of Denying a Conjunct" ], "current_concepts": [ "Symbolic Translation", "Argument Validity", "Disjunctive Syllogism" ] } ## Translate the premises and conclusion into symbolic form $$ \begin{aligned} &\text{Let } p: \text{"The bug is dead."} \ &\text{Let } q: \text{"The bird is white."} \ &\text{Premise 1: } p \lor q \quad (\text{"The bug is dead or the bird is white."}) \ &\text{Premise 2: } eg p \quad (\text{"The bug is not dead." - noting the typo "bud" in the prompt as } p) \ &\text{Conclusion: } eg q \quad (\text{"Therefore, the bird is not white."}) \end{aligned} $$ ## Analyze the validity of the argument form $$ \begin{aligned} &\text{Argument Form:} \ &p \lor q \ & eg p \ &\hline \ &\therefore eg q \ \ &\text{Under Disjunctive Syllogism, the valid inference from } p \lor q \text{ and } eg p \text{ is } q. \ &\text{Since the conclusion is } eg q \text{ instead of } q, \text{ the argument is invalid.} \end{aligned} $$ ## Verify with a counterexample truth assignment $$ \begin{aligned} &\text{Let } p = \text{False (F)}, q = \text{True (T)}: \ &\text{Premise 1: } p \lor q \equiv \text{F} \lor \text{T} \equiv \text{T} \ &\text{Premise 2: } eg p \equiv eg\text{F} \equiv \text{T} \ &\text{Conclusion: } eg q \equiv eg\text{T} \equiv \text{F} \ &\text{Since both premises are true but the conclusion is false, the argument is invalid.} \end{aligned} $$

(A) Valid

(B) Invalid

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Argument Validity" ] }

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QUESTION IMAGE

Question

Explanation:

Translate the premises and conclusion into symbolic form

Analyze the validity of the argument form

Verify with a counterexample truth assignment

Answer: