an argument is represented below.

premise 1: if the bananas are ripe, then ill make banana bread.
premise 2: the bananas are not ripe.
conclusion: i wont make banana bread.

assume $p$ represents \the bananas are ripe\ and $q$ represents the statement \ill make banana bread.\

a. write premise 1 in symbolic notation:
b. write premise 2 in symbolic notation:
c. write the conclusion in symbolic notation:
d. use a truth table to evaluate the argument. is this argument valid?
yes, this argument is valid.
no, this answer is invalid.

Question

an argument is represented below.

premise 1: if the bananas are ripe, then ill make banana bread.
premise 2: the bananas are not ripe.
conclusion: i wont make banana bread.

assume $p$ represents \the bananas are ripe\ and $q$ represents the statement \ill make banana bread.\

a. write premise 1 in symbolic notation:
b. write premise 2 in symbolic notation:
c. write the conclusion in symbolic notation:
d. use a truth table to evaluate the argument. is this argument valid?
yes, this argument is valid.
no, this answer is invalid.

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Symbolic Logic Translation", "Argument Validity" ], "new_concepts": [], "current_concepts": [ "Symbolic Logic Translation", "Conditional Statements", "Argument Validity", "Symbolic Arguments" ] } ## Translate premises and conclusion to symbolic form $$ \begin{aligned} &\text{Premise 1: } p ightarrow q \ &\text{Premise 2: } \sim p \ &\text{Conclusion: } \sim q \end{aligned} $$ ## Evaluate argument validity using truth table $$ \begin{array}{cc|c|c|c} p & q & p ightarrow q & \sim p & \sim q \ \hline \text{T} & \text{T} & \text{T} & \text{F} & \text{F} \ \text{T} & \text{F} & \text{F} & \text{F} & \text{T} \ \text{F} & \text{T} & \text{T} & \text{T} & \text{F} \ \text{F} & \text{F} & \text{T} & \text{T} & \text{T} \end{array} $$ ## Determine validity from critical rows $$ \begin{aligned} &\text{Critical row where both premises } (p ightarrow q) \text{ and } (\sim p) \text{ are True: Row 3 } (p = \text{F}, q = \text{T}) \ &\text{In Row 3, the conclusion } (\sim q) \text{ is False.} \ &\text{Therefore, the argument is invalid (Fallacy of Denying the Antecedent).} \end{aligned} $$ ## Question a Write Premise 1 in symbolic notation: $p ightarrow q$ ## Question b Write Premise 2 in symbolic notation: $\sim p$ ## Question c Write the Conclusion in symbolic notation: $\sim q$ ## Question d Yes, this argument is valid.

No, this answer is invalid.

{ "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Symbolic Arguments" ] }

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QUESTION IMAGE

Question

Explanation:

Translate premises and conclusion to symbolic form

Evaluate argument validity using truth table

Determine validity from critical rows

Answer:

Question a

Question b

Question c

Question d