A polygon is regular or a polygon has a side which is longer than another side of the polygon. If a polygon is regular then all the sides of the polygon are congruent. If a polygon has one side which is longer than another side of the polygon, then an interior angle of the polygon has measure greater than one of the interior angles of the polygon. Therefore, either the polygon have congruent sides or an interior angle of the polygon has a measure greater than on

Q: Consider the conditional statement shown If a parallelogram has four right angles, then it is a…

A: The given statement is "If a parallelogram had four right angles, then it is a square."

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Q: Use Valid Argument Forms (i.e., Modus Ponens, etc.) to deduce the conclusion from the premises. Give…

A: Given the premises   1 P→Q2 R∨S3 ~S→~L4 ~Q∨S5 ~S6 ~P∧R→U7 W∨L Prove U∧W.

Q: 31. If both of the statements below are true, which statement is a logical conclusion? Some…

A: We need to see which one of the following conclusions we can draw from the given statements.  We…

Q: L- Use truth tables to show the stetenant P-> cQ1 R) s equivalet to the ftatemfrt P =Q)^ P R)

A: Given the statement P→(Q∧R)=(P→Q)∧(P→R).We need to prove the above statement using truth table.

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A: If two triangles are congruent, then each part of the triangle (side or angle) is congruent to the…

Q: How many of the following propositions are false a) There are non-similar congruent triangles b)…

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Q: B. Write a conclusion based on the two true statements given using the La of Detachment or the Law…

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Q: 2. Make the following assumptions and find the truth value of the given compounds. A is true, B is…

A: Since we only answer up to 3 subparts, we'll answer the first 3. Please resubmit the question and…

Q: Which of the following statements are true about inductive reasoning? * L. All forms of inductive…

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Q: A. Rewrite each conditional statement in if-then form. 1. A rectangle is a parallelogram with four…

A: The given question is solved below.

Q: Use the standard forms of valid and invalid arguments to determine the validity of the arguments.…

A: Since you have posted a question with multiple subparts according to guildlines I will solve first…

Q: Write in symbolic form then determine the validity of an argument using truth table. Show neat and…

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Q: onstruct a Truth Table A. (p ^q) → p pap ^q→p B. p ^ ( q v r ) Û (p^q) v ( p ^r ) pgrp ^(q v r )ºp ^…

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Q: If the scalene triangles AMAT=ALOV, determine the truth value of the following congruence statements…

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Q: What statement is the converse of the following conditional? A triangle has three angles.   Select…

A: Here we have to select which statement is the converse of the given conditionals.

Q: Identify p and q. • Then use the Law of Detachment and a truth table to determine if the argument is…

A: By the law of detachment if the two statements are true then we can form a third true statement

Q: Consider the following statement. Every parallelogram is a quadrilateral. (a) Write the converse of…

A: We can find the converse , inverse and contrapositive as below.

Q: What conclusion can be drawn from the following statement by using the law of detachment? If a…

A: We have to solve the problem

Q: DETERMINE WHICH CONDITIONAL STATEMENTS WOULD PRODUCE EQUIVALENT STATEMENTS 12. If a segment is…

A: The answers are given below.

Q: 8. Now it's your turn. Use the same logical approach to prove that the other pair of vertical…

A: Proof of vertical angle theorem.

Q: Construct a Truth table Write the implications and their connections (converse, inverse and…

A: Given an if-then statement " if p, then q," we can create three related statements :…

Q: Given the following biconditional statement: "A quadrilateral is a square if and only if it has four…

A: we have to given biconditional statement for the given statement

Q: Determine whether the given argument is valid or not using Euler Circles. Some students are…

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Q: DETERMINE WHICH CONDITIONAL STATEMENTS WOULD PRODUCE EQUIVALENT STATEMENTS 7. If a triangle is…

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Q: Identify p and q. • Then use the Law of Detachment and a truth table to determine if the argument is…

A: Proposition : It is a declarative statement which is either true or false.  Argument :  It is a…

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

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

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Q: ASA, SAS, AAS, RHS) Congruence Complete the following sentences: a) Two triangles are congruent if…

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Q: The truth table for (pv g) v (pAr) is the same as the truth table for OA (pA q) v p O B. (p v q) ^ (…

A: In this question we have to find which truth table is same as the given truth table.

Q: A valid argument is given below. Fill in the missing values of the proof. 1. (A) Hypothesis r- -t 2.…

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Q: If you exclude all the lines that are premises, how many lines does the shortest proof of the…

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Q: 1. Which of the following statement relates triangles to quadrilaterals? a. Triangles and…

A: Consider the given: a) Triangles and quadrilateral are classified according to sides and angles.…

Q: [(p^~q) v~r] ^ (q^r)

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Q: Use the law of syllogism to write a new conditional that follows from the pair of given statements:…

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Q: Convert the following if-then statement to converse,inverse and contrapositive.  • If a number ends…

A: Converse, Inverse and Contrapositive: Now we can define the converse, the inverse and the…

Q: B. Write the converse, the inverse, and the contrapositive of the following conditional statements.…

A: H   ,

Q: QUESTION 5 What is the converse of this conditional statement: "If the table top is rectangular,…

A: Since you have posted a multiple question according to guildlines I will solve first question(Q5)…

Q: I. Determine whether each of the following argument is an example of Inductive Reasoning or…

A: As per our guidelines we are supposed answer only one questions (3 subparts) rest can be reposted

Q: B. Write the converse, inverse, and contrapositive for each statement. 1. If a polygon has four…

A: 1.If a polygon has four sides , then it is a quaddrilateral.1.If a rained last night, then the…

Q: Direction: On a piece of paper (or through any gadget or app for writing/drawing), create the truth…

A: Given: Let us consider the given compound statements, 1. ~p⊕q→~r→p∨r↔~q 2. q∨r↔~p∧q⊕~r→~p Let's…

Q: The respective truth values of the following statements are: a) If the diagonals of a quadrilateral…

A: To find the truth values, we need to confirm if the given statement is true or false.

Q: Is this argument valid, sound, or invalid? Premise:  All cups are green Premis:  Socrates is a cup.…

A: The given argument is as follows. Premise: All cups are green Premise: Socrates is a cup.…

Q: Given, "If angles are congruent, then the measures of the angles are equal." Identify the…

A: Given, "If angles are congruent, then the measures of the angles are equal."  We need to identify…

Q: Determine if the following are TRUE or FALSE:   A quadrilateral is a rectangle if and only the…

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Q: Write in symbolic form then determine the validity of an argument using truth table.  A polygon is…

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Q: Use truth tables to determine whether the following arguments are valid : The price of vil will…

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Q: Consider the following statement. Every parallelogram is a quadrilateral. (a) Write the converse of…

A: a) A converse of a given statementinvolves the interchanging of hypothesis and theconclusion in the…

Q: Boardwork: Determine the truth value of the compound statement given that Pis FALSE, Q is TRUE and R…

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Q: I. Construct the converse, inverse and contrapositive of the conditional statement, and identify…

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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.