De Morgan Laws 1q v r) = -qA-r • Intuition-For the LHS to be true: neither q nor r can be true. This is the same as saying q and r must be false. • -(q Ar) =-V-r • Intuition - For the LHS to be true: qAr must be false. This is the same as saying q or r must be false. • Proof: use truth tables

Q: III. Prove or disprove using truth table. 1.) (-q V p) ++r= (¬p^q) +r 2.) - p → (q V r)) = p^…

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Q: Let p represent a true statement, let q represent a true ​statement, and let r represent a false…

A: follow next step

Q: we let s =“4 is irrational.” and t = “4 is even.” Determine the truth value of the statement: s →t.…

A: Every irrational number is not even.

Q: Answer the following and show your solutions: 1. Suppose that the statement p-a is false. Find all…

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Q: O Consider a) p → -q, ~p →q pq. Show it is sound. conclusion must also be true. Need truth-tables to…

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Q: If p is false and q is true, find the truth value of the statement. -(p v q) → -p Select the truth…

A: p q p∨q ~p∨q ~p ~p∨q→~p T T T F F T T F T F F T F T T F T T F F F T T T

Q: Let p, q, r be true. Determine whether the ff statements can have the given truth value (in…

A: Truth table for some operations:-  p q ~p p∨q p∧q p→q p↔q T T F T T T T T F F T F F F F T T…

Q: - (pA(-p V 9) A(-9V -p)}

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Q: Construct a truth table for the statements below a. (p ∧ q) ∧ (~r ∨ q). b. ~[~p ∧ (q ∧ r)] c. [p ∧…

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Q: Given the proposition: I will be lonely if and only if I am lazy and does not exercise. What can you…

A: Logic

Q: 3. [ (P - Q) A (Q– R) ] - (-Q - -R) Q|R| P-Q (P - Q) A (Q → R) -Q R -R -Q- -R[(P-Q) A (Q -R) ]- (-Q…

A: P→Qis False if and only if P is True and Q is False P∧Q is True if and only if both P and Q are True

Q: "all mathematics teachers have a strange sense of humor. alex is a mathematics teacher."

A: Let A = Alex is a mathematics teacher.    B = All mathematics teacher have a strange sense of humor.…

Q: Draw the conclusion from the following premises using a formal proof (Rules of inference). • If the…

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Q: If p is false, q is false, and r is true, find the truth value of the statement below.…

A: making table and solving easily breaking the given logical operation and by using and ,…

Q: 2) Consider the rules of inference: a)p → ~q, ~p →q Poq. Show it is sound. Recall we need to show…

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Q: Suppose p, q, andr are propositions. Let the expression (p --> q) -->r be a contradiction. Which of…

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Q: •p -q and -p v q are logically equivalent. •p -q =-p v q • Truth tables are the simplest way to…

A: Two statements  P and  Q are logically equivalent it means that provided P is true precisely when Q…

Q: Suppose p is false and (p→s)↔(r∧q) is true . Find the truth values of r and s.

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Q: Given that p and q are True and r and s are False, find the truth value of the statement. (~r) ⇒…

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Q: If p is true, q is true, and r is true, find the truth value of the statement. (-p+r) A (-+ r) .....…

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Q: Let p represent a true ​statement, and let q represent a true statement. Find the truth value of the…

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Q: (r\V -p) V[((p V -q) → (q → r)]

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Q: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and…

A: In the following * means complement so z* means "not Z" Assign a binary variable to each person.…

Q: Given: If A and B, then C. Given: The if-then statement's reverse is also correct. If A is True, B…

A: This is logic based question

Q: q: It is Saturday. Write each statement below in symbolic form using p and q. Descriptive form…

A: Write each statement below in symbolic form using p and qStatement 1: If it is not Saturday then we…

Q: а. (pVq) л~ r b. p V (~ q ^~ r)

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Q: Find the truth value of ~ (q →r) ^ p given that p and r are true, and q is false.   By De Morgan’s…

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Q: 3.2 EXERCISES Use the concepts introduced in this section to answer Exercises 1-6. If q is false,…

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Q: If p and q are false and r is true, determine the truth value of the following Statement Truth Value…

A: Given : p and q are false and r is true.

Q: The statement (PA~ B) = B V Q is false. Find the truth values of P,Q, & B

A: Given that the statement P∧~B⇒B∨Q is false.

Q: [(pV -q) A(-r^q] V (r^-p)

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Q: 1. Determine the truth value of the compound statement given that p is a false statement, q is a…

A: We will solve it by Truth Table a) p q r ~p ~p∨q r∧(~p∨q) T T T F T T T T F F T F T F T F F…

Q: 8. (P Q) ^ (Q-P) and P+ Q have the same truth values. 9. If P is false and Q is true, then PQ is…

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Q: VIII. Supply the missing statement and reason. Given: AR = MS A R Prove: AM - RS Statements Reasons…

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Q: the truth value of e and f is unknown, determine the truth value of the folloWnĘ propositions (if…

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Q: Make a truth table for the statement ¬Q V (Q → P)) P Q ¬Q Q → P ¬Q v (Q → P)) F F T F What can you…

A: We will find out the required value.

Q: 3. Suppose p and q represent false statements, while r represents true statement. Find the truth…

A: As per the guidelines, we are supposed to answer only one question. Kindly repost the other…

Q: If p is true, q is true, and r is true, find the truth value of the statement. (p v q) (q v r)…

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Q: Solve the following questions. Show your solutions completely and clearly. 1. The following is a…

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Q: Which logical expression is a contradiction? (hint: you might want to draw a truth table) 1. (p V q)…

A: By the help of truth table we prove the results.

Q: 1. [(-p A q) → (-r V s)] → [t A -(a v b)] p:T , q:T , r : F , s:F, t:F ,a:F , b: T 2. -(p v q) A…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Suppose P is false and that the statement (RS) → (PAQ) is true. Find, without using a truth table,…

A: Disclaimer:  Since you have asked multiple question, we will solve the first question for you. If…

Q: Supposethat the statement p>¬qis false. Find all combinations of truth values of r and s for which…

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Q: 2. Let the statement p be true and q be false. What are the truth values of the following? Show all…

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Q: 3 a) Lse truth taible. can we conclude p + q) and p Aq are logical equivalent or ne cach step must…

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Q: 3. [pa(~q)]v[(~p)vq] In order to find the number of rows to create, use the formula 2", where n is…

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Q: If p is true and q is true, find the truth value of the statement. -(p v q) → -p Select the truth…

A: We have to check

Q: Identify the correct steps involved while proving (p v ¬g) ^ (q v¬ (rv -p) is true when p, q, and r…

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Q: 26. a. Make a truth table for ~(p ^ q). Make another truth table for ~p V ~q. b. Make a truth table…

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Q: If p is true, q is true, and r is true, find the truth value of the statement. (p v q)(q v -r)…

A: Given that  p is true q is true r is true then we have to find truth table of the statement…

Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.