QUESTION 5What is the converse of this conditional statement: "If the table top is rectangular, then its diagonals are congruent."O If the diagonals of a table top are congruent, then it is rectangular.O If the table top is rectangular, then its diagonals are congruent.O If the table top is not rectangular, then its diagonals are not congruent.O If the diagonals of a table top are not congruent, then it is not rectangular.QUESTION 6What is the inverse of this conditional statement: "If the table top is rectangular, then its diagonals are congruent."O If the diagonals of a table top are congruent, then it is rectangular.O If the table top is rectangular, then its diagonals are congruent.If the table top is not rectangular, then its diagonals are not congruent.Q If the diagonals of a table top are not congruent, then it is not rectangular. QUESTION 7What is the contrapositive of this conditional statement: "If the table top is rectangular, then its diagonals are congruent."O If the diagonals of a table top are congruent, then it is rectangular.O If the table top is rectangular, then its diagonals are congruent.O If the table top is not rectangular, then its diagonals are not congruent.O If the diagonals of a table top are not congruent, then it is not rectangular.QUESTION 8If the conditional statement is true, then theis also logically true.converseinverseO biconditionalcontrapositive

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

Answered: QUESTION 5 What is the converse of this…

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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Write each of the following conditional statements and the corresponding converse, inverse, and contrapositive as English sentences in the form “if ?, then ?.”Example: Whenever it rains, it pours. Answer: Original statement: If it rains, then it pours. Converse: If it pours, then it rains. Inverse: If it doesn’t rain, then it doesn’t pour. Contrapositive: If it doesn’t pour, then it doesn’t rain. 1.1 You can do it if you put your mind to it. 1.2 Being cold implies that you need a jacket. 1.3 Petting the cat is sufficient for it to purr.
A conditional is a statement that contains a conjecture. O True O False
Suppose that the given statements are true. Find the other true statements. (a) Given: If the window is above the door, then Austin's cousin is a girl. Which statement must also be true? - If Austin's cousin is a girl, then the window is above the door. - If Austin's cousin is not a girl, then the window is not above the door. - If the window is not above the door, then Austin's cousin is not a girl. (b) Given: If the bike is fast, then Rachel sleeps on the floor. The bike is fast. Which statement must also be true? - The bike is not fast. - Rachel sleeps on the floor. - Rachel does not sleep on the floor. (c) Given: If David knows how to dance, then the tires are old. If the tires are old, then my favorite movie is being shown. Which statement must also be true? - If my favorite movie is being shown, then the tires are old. - If David knows how to dance, then my favorite movie is being shown. - If my favorite movie is being shown, then David knows how to…
Which statement is the inverse of the conditional statement below? “If tomorrow is Monday, then today is Sunday.” Select one: a. If today is Sunday, then tomorrow is Monday. b. If tomorrow is not Monday, then today is not Sunday. c. If today is not Sunday, then tomorrow is not Monday. d. If tomorrow is Sunday, then today is not Monday.
Which of these statements is logically equivalent to "You don't Love Hamburger or you are not American if you don't love Donuts"? Select one: O a. If you love Donuts then you are American and love Hamburger O b. You don't love Donuts, or you are American and love Hamburger O c. Both Answers
Consider the construction of a vending machine's logic. Assume that every soda costs a quarter, and that the machine accepts only quarters. E = True indicates the machine is empty, it has no more sodas S = True indicates the user has made a selection P = True indicates the user has paid a quarter The machine may send two control commands to its machinery: V = True indicates machine will give the user a soda (i.e. "vend") R = True indicates machine will return the user's quarter The machine should return a user's quarter only when they have paid and the machine is empty. The machine should give a soda only when a user has paid, made a selection and the machine is not empty.
b) Determine if the statement below is true or false, and explain your reasoning. If two statements are logically equivalent, then so are their negations.

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