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Refer to the following statement to answer parts (a) through (c) below. The mathematician is intelligent and an overachiever, or not an overachiever. a. Write the statement in symbolic form. Assign letters to simple statements that are not negated. Choose the correct answer b O A. let p = The mathematician is intelligent and let q = The mathematician is an overachiever; (p^ q) v ~q O B. let p = The mathematician is intelligent and let q = The mathematician is not an overachiever; (p ^ q) v ~ q O C. let p = The mathematician is intelligent and let q = The mathematician is an overachiever; (p v q) ^ ~q O D. let p = The mathematician is intelligent and let q = The mathematician is not an overachiever; (p v q) ^ - q b. Construct a truth table for the symbolic statement in part (a). p^q -q (p ^ q) v -q Р T T F LL q T LL T FF ▶ ▶ ▶

Refer to the following statement to answer parts (a) through (c) below. The mathematician is intelligent and an overachiever, or not an overachiever. a. Write the statement in symbolic form. Assign letters to simple statements that are not negated. Choose the correct answer b O A. let p = The mathematician is intelligent and let q = The mathematician is an overachiever; (p^ q) v ~q O B. let p = The mathematician is intelligent and let q = The mathematician is not an overachiever; (p ^ q) v ~ q O C. let p = The mathematician is intelligent and let q = The mathematician is an overachiever; (p v q) ^ ~q O D. let p = The mathematician is intelligent and let q = The mathematician is not an overachiever; (p v q) ^ - q b. Construct a truth table for the symbolic statement in part (a). p^q -q (p ^ q) v -q Р T T F LL q T LL T FF ▶ ▶ ▶

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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there one part c of the solution it will be in the next question 

**Mathematical Logic Exercise: Translating Statements and Constructing Truth Tables** **Statement Translation Task** Refer to the statement below to complete parts (a) and (b). **Given Statement:** "The mathematician is intelligent and an overachiever, or not an overachiever." **a. Translating the Statement into Symbolic Form** Assign letters to simple statements without negation. Select the correct symbolic representation. - **Option A:** Let \( p \) = "The mathematician is intelligent" and let \( q \) = "The mathematician is an overachiever." Symbolic form: \( (p \land q) \lor \sim q \) - **Option B:** Let \( p \) = "The mathematician is intelligent" and let \( q \) = "The mathematician is not an overachiever." Symbolic form: \( (p \land q) \lor \sim q \) - **Option C:** Let \( p \) = "The mathematician is intelligent" and let \( q \) = "The mathematician is an overachiever." Symbolic form: \( (p \lor q) \land \sim q \) - **Option D:** Let \( p \) = "The mathematician is intelligent" and let \( q \) = "The mathematician is not an overachiever." Symbolic form: \( (p \lor q) \land q \) **Correct Answer:** Option A – Symbolic form: \( (p \land q) \lor \sim q \) **b. Constructing a Truth Table** Create a truth table for the symbolic statement in part (a). | \( p \) | \( q \) | \( p \land q \) | \( \sim q \) | \( (p \land q) \lor \sim q \) | |---------|---------|-------------------|--------------|--------------------------------| | T | T | T | F | T | | T | F | F | T | T | | F | T | F | F | F | | F | F | F | T | T | - **\( p \land q \):** "The mathematician is intelligent and an overachiever."
Transcribed Image Text:**Mathematical Logic Exercise: Translating Statements and Constructing Truth Tables** **Statement Translation Task** Refer to the statement below to complete parts (a) and (b). **Given Statement:** "The mathematician is intelligent and an overachiever, or not an overachiever." **a. Translating the Statement into Symbolic Form** Assign letters to simple statements without negation. Select the correct symbolic representation. - **Option A:** Let \( p \) = "The mathematician is intelligent" and let \( q \) = "The mathematician is an overachiever." Symbolic form: \( (p \land q) \lor \sim q \) - **Option B:** Let \( p \) = "The mathematician is intelligent" and let \( q \) = "The mathematician is not an overachiever." Symbolic form: \( (p \land q) \lor \sim q \) - **Option C:** Let \( p \) = "The mathematician is intelligent" and let \( q \) = "The mathematician is an overachiever." Symbolic form: \( (p \lor q) \land \sim q \) - **Option D:** Let \( p \) = "The mathematician is intelligent" and let \( q \) = "The mathematician is not an overachiever." Symbolic form: \( (p \lor q) \land q \) **Correct Answer:** Option A – Symbolic form: \( (p \land q) \lor \sim q \) **b. Constructing a Truth Table** Create a truth table for the symbolic statement in part (a). | \( p \) | \( q \) | \( p \land q \) | \( \sim q \) | \( (p \land q) \lor \sim q \) | |---------|---------|-------------------|--------------|--------------------------------| | T | T | T | F | T | | T | F | F | T | T | | F | T | F | F | F | | F | F | F | T | T | - **\( p \land q \):** "The mathematician is intelligent and an overachiever."
Refer to the following statement to answer parts (a) through (c) below. The mathematician is intelligent and an overachiever, or not an overachiever. --- **b. Construct a truth table for the symbolic statement in part (a).** | p | q | p ∧ q | ¬q | (p ∧ q) ∨ ¬q | |-----|-----|-------|-----|--------------| | T | T | | | | | T | F | | | | | F | T | | | | | F | F | | | | **c. Use the truth table to indicate one set of conditions that make the compound statement true, or state that no such conditions exist.** - ○ A. The statement is true when p is true and q is false. - ○ B. The statement is true for all conditions. - ○ C. The statement is true when p is true or q is false.
Transcribed Image Text:Refer to the following statement to answer parts (a) through (c) below. The mathematician is intelligent and an overachiever, or not an overachiever. --- **b. Construct a truth table for the symbolic statement in part (a).** | p | q | p ∧ q | ¬q | (p ∧ q) ∨ ¬q | |-----|-----|-------|-----|--------------| | T | T | | | | | T | F | | | | | F | T | | | | | F | F | | | | **c. Use the truth table to indicate one set of conditions that make the compound statement true, or state that no such conditions exist.** - ○ A. The statement is true when p is true and q is false. - ○ B. The statement is true for all conditions. - ○ C. The statement is true when p is true or q is false.
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