(c) Determine if the following statement is a tautology. Ensure that you explain the stepstaken and the reason for your decision.(p q r) → ((p v q v r) ^ ¬((p ^r) v (q ^r) v (p ^ q)))

We will use the truth table method to check whether given statement is tautology or not. If in last…

Answered: (c) Determine if the following…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 56E

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Using the image below; (i) Determine if the following statement is tautology: (ii) if yes or no, state the reason why
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Let P(x, y) be the predicate "musician a has hit y". The domain for the a variables consists of all musicians. The domain for the y variables consists of all hits. Express the quantification 3x, yi, Vyz, (P(x, y₁)^((y2 #y₁)→ P(x, y2))) as an English sentence. O There are two distinct musicians that do not have the same hit. O Every musician has a unique hit. O Every musician has at least two hits. O Every two distinct musicians do not have the same hit. There is a musician that has a unique hit. There is a musician that has at least two hits. Now let Q(x, y) be the predicate "game x has winner y. The domain for the a variables consists of all games. The domain for the y variables consists of all winners. Express the quantification 3x₁, x2, Vy, ((1 22₂) ^ (Q(x, y) ^ Q(x2, y))) as an English sentence. There are two distinct games that do not have the same winner. O Every game has a unique winner. O Every two distinct games do not have the same winner. There is a game that has at least…
B. Show that each of the following are logically equivalent. 1. p ^ (q v r) = (p ^ q) v (p ^ r). s 2. -(p A q) = -p V ¬q
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(c) Determine if the following statement is a tautology. Ensure that you explain the steps taken and the reason for your decision. (pqr) → ((pvqvr)^((p^r) V (q^r) v (p^q)))