### Truth Table and Disjunctive Logical Statements**Truth Table for $ f(p, q, r) $:**| $ p $ | $ q $ | $ r $ | $ f(p, q, r) $ ||---------|---------|---------|------------------|| T | T | T | T || T | T | F | T || T | F | T | F || T | F | F | F || F | T | T | F || F | T | F | T || F | F | T | F || F | F | F | F |**Disjunctive Logical Statement Options:**Select the disjunctive logical statement that represents $ f(p, q, r) $:- **A.** $ (p \land q \land r) \lor (\lnot p \land q \land \lnot r) \lor (p \land q \land \lnot r) $- **B.** $ (p \land \lnot q \land r) \lor (p \land \lnot q \land \lnot r) \lor (\lnot p \land q \land r) \lor (\lnot p \land \lnot q \land r) \lor (\lnot p \land \lnot q \land \lnot r) $- **C.** $ (p \lor q \lor r) \land (\lnot p \lor q \lor \lnot r) \lor (p \lor q \land \lnot r) $- **D.** $ (\lnot p \land \lnot q \land \lnot r) \lor (p \land \lnot q \land r) \lor (\lnot p \land \lnot q \land r) $**Explanation of Graphs/Diagrams:**This is a standard truth table that visually represents all possible combinations of truth values for logical variables $ p $, $ q $, and $ r $ along with the corresponding output for the function $ f(p, q, r) $. Each row represents a different combination of truth values for

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Description: ### Truth Table and Disjunctive Logical Statements**Truth Table for $ f(p, q, r) $:**| $ p $ | $ q $ | $ r $ | $ f(p, q, r) $ ||---------|---------|---------|------------------|| T | T | T | T || T |

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Consider the following truth table. pqrf(p,q,r) TTT TTF T TFT F TFF F FTT F EITE FFT F FIFF F Give a disjunctive logical statement to represent f(p, q, r). A. (p Aq Ar) V (-p^q^ ¬r) V (p ^q^ ¬r) B. (p A -q A r) V (p^ ¬qr) V (-p^q^r) V (-p ^ ¬q ^ r) V (-p A ¬q^ -r) c. (p V q V r) A (-p V q V ¬r) A (pV q V ¬r) D. (-pA ng A -r) V (p^ ¬qA r) V (-p^ ¬qAr)

Consider the following truth table. pqrf(p,q,r) TTT TTF T TFT F TFF F FTT F EITE FFT F FIFF F Give a disjunctive logical statement to represent f(p, q, r). A. (p Aq Ar) V (-p^q^ ¬r) V (p ^q^ ¬r) B. (p A -q A r) V (p^ ¬qr) V (-p^q^r) V (-p ^ ¬q ^ r) V (-p A ¬q^ -r) c. (p V q V r) A (-p V q V ¬r) A (pV q V ¬r) D. (-pA ng A -r) V (p^ ¬qA r) V (-p^ ¬qAr)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Topic Video

Question

### Truth Table and Disjunctive Logical Statements

**Truth Table for $ f(p, q, r) $:**

| $ p $ | $ q $ | $ r $ | $ f(p, q, r) $ |
|---------|---------|---------|------------------|
| T | T | T | T |
| T | T | F | T |
| T | F | T | F |
| T | F | F | F |
| F | T | T | F |
| F | T | F | T |
| F | F | T | F |
| F | F | F | F |

**Disjunctive Logical Statement Options:**

Select the disjunctive logical statement that represents $ f(p, q, r) $:

- **A.** $ (p \land q \land r) \lor (\lnot p \land q \land \lnot r) \lor (p \land q \land \lnot r) $

- **B.** $ (p \land \lnot q \land r) \lor (p \land \lnot q \land \lnot r) \lor (\lnot p \land q \land r) \lor (\lnot p \land \lnot q \land r) \lor (\lnot p \land \lnot q \land \lnot r) $

- **C.** $ (p \lor q \lor r) \land (\lnot p \lor q \lor \lnot r) \lor (p \lor q \land \lnot r) $

- **D.** $ (\lnot p \land \lnot q \land \lnot r) \lor (p \land \lnot q \land r) \lor (\lnot p \land \lnot q \land r) $

**Explanation of Graphs/Diagrams:**

This is a standard truth table that visually represents all possible combinations of truth values for logical variables $ p $, $ q $, and $ r $ along with the corresponding output for the function $ f(p, q, r) $. Each row represents a different combination of truth values for

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Let P(a, b) and Q(a, b) be the open sentences defined by P(a, b) : a = b andQ(a, b) : a^2 − b^2 = 0, respectively, where the variables a and b can take any value in Z. Determine the truth value of the open sentence Q(a, b) ⇒ P(a, b) for each (a, b) ∈ {(2, −2),(5, 7),(3, 3)}. Explain your answers. (Z is the set of intergers)