Sloppy Sam is trying to prove a certain proposition P. He defines two related propositions and...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Sloppy Sam is trying to prove a certain proposition P. He defines two related propositions and R, and then proceeds to prove four implications: R⇒Q, Q⇒R, R⇒P, P⇒ Q. He then reasons as follows If Q is true, then since I proved Q⇒ R, I can conclude that R is true. Now, since I proved R⇒ P, I can conclude that P is true. Similarly, if R is true, then P is true and so Q is true. Likewise, if P is true, then so are Q and R. So any way you look at it, all three of P, Q, and R are true. (a) Exhibit truth tables for and for (PQ) ^ (Q⇒ R) ^ (R⇒P), (1) PAQAR. (2) Use these tables to find a truth assignment for P, Q, R so that (1) is T and (2) is F. (b) You show these truth tables to Sloppy Sam and he says "OK, I'm wrong that P, Q and R all have to be true, but I still don't see the mistake in my reasoning. Can you help me understand my mistake?" How would you explain to Sammy where the flaw lies in his reasoning? Sloppy Sam is trying to prove a certain proposition P. He defines two related propositions and R, and then proceeds to prove four implications: R⇒Q, Q⇒R, R⇒P, P⇒ Q. He then reasons as follows If Q is true, then since I proved Q⇒ R, I can conclude that R is true. Now, since I proved R⇒ P, I can conclude that P is true. Similarly, if R is true, then P is true and so Q is true. Likewise, if P is true, then so are Q and R. So any way you look at it, all three of P, Q, and R are true. (a) Exhibit truth tables for and for (PQ) ^ (Q⇒ R) ^ (R⇒P), (1) PAQAR. (2) Use these tables to find a truth assignment for P, Q, R so that (1) is T and (2) is F. (b) You show these truth tables to Sloppy Sam and he says "OK, I'm wrong that P, Q and R all have to be true, but I still don't see the mistake in my reasoning. Can you help me understand my mistake?" How would you explain to Sammy where the flaw lies in his reasoning?
Expert Answer:
Related Book For
Management and Cost Accounting
ISBN: 978-1405888202
4th edition
Authors: Alnoor Bhimani, Charles T. Horngren, Srikant M. Datar, George Foster
Posted Date:
Students also viewed these mathematics questions
-
In April 1992, EuroDisney SCA opened its doors to European visitors. Located by the river Marne some 20 miles east of Paris, it was designed to be the biggest and most lavish theme park that Walt...
-
Read the case study "Southwest Airlines," found in Part 2 of your textbook. Review the "Guide to Case Analysis" found on pp. CA1 - CA11 of your textbook. (This guide follows the last case in the...
-
The Crazy Eddie fraud may appear smaller and gentler than the massive billion-dollar frauds exposed in recent times, such as Bernie Madoffs Ponzi scheme, frauds in the subprime mortgage market, the...
-
Let a function f be the line graph connecting the data points (1, 2), (4,9), and (6,3). (a) Write the formula for a piecewise-linear function f that passes through these data points whose domain is 1...
-
If the resultant force acting on the bracket is required to be a minimum, determine the magnitudes of F 1 and the resultant force. Set ? = 30?. 30 F= 200 N 13 12 F, 260 N
-
A freshman studentat the University (Jane Smith) goes out to a local bar off of campus after mid term exams. While there she meets a guy name Jack Johnson. Johnson is studying at the local community...
-
What procedures can be used to determine whether all transactions that should be recorded are recorded?
-
Superior Uniforms produces uniforms. The company allocates manufacturing overhead based on the machine hours each job uses. Superior Uniforms reports the following cost data for the past year:...
-
What characteristics of market structure make quality competition more likely than price competition? Which type of competition is more desirable from the viewpoint of the consumer? Why has the...
-
The CyClon project team has started gathering information necessary to develop a project network-predecessor activities and activity time in days. The results of their meeting are found in the...
-
Mike Reynolds has four assignments due in class tomorrow, and his class times are as follows: Time Class OM 304 Marketing 385 Psychology 216 Finance 200 9 a.m. 12 p.m. 3 p.m. 6:30 p.m. Each class...
-
The \(\mathrm{dB}\) (Bode plot) of transfer function \(\mathrm{G}(\mathrm{s})\) is shown in figure below. Now, consider the following statements. I. \(\mathrm{G}(s)\) has corner frequencies at...
-
Find decoupled state equations for the system described as \[ \begin{aligned} {\left[\begin{array}{l} \dot{x}_{1} \\ \dot{x}_{2} \end{array}ight] } & =\left[\begin{array}{rr} 0 & 1 \\ -6 & -5...
-
Construct phase variable form simulation diagram for the following transfer functions and develop state space model in matrix form (a) \(\mathrm{T}(s)=\frac{\mathrm{Y}(s)}{\mathrm{U}(s)}=\frac{10...
-
The SISO system with repeated characteristic roots is described by transfer function \[ \mathrm{T}(s)=\frac{\mathrm{Y}(s)}{\mathrm{U}(s)}=\frac{7 s^{3}}{(s+2)^{2}(s+6)^{2}} \] Find state space model...
-
For the system described by the state equation \[ \dot{x}=\left[\begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0.5 & 1 & 2 \end{array}ight] x+\left[\begin{array}{l} 0 \\ 0 \\ 1 \end{array}ight] u \] if...
-
You are evaluating two possible stock investments , Leverage Co. and Value Corp. Leverage Co. has an expected return of 10 % and a beta of 1.4 . Value Corp , has an expected return of % and a beta of...
-
Sandcastles, Inc.s management has recently been looking at a proposal to purchase a new brick molding machine. With the new machine, the company would not have to buy bricks. The estimated useful...
-
Bellingwolde BV operates car rental agencies at over 20 airports. Customers can choose from one of three contracts for car rentals of one day or less: Contract 1: 50 for the day Contract 2: 30 for...
-
Why is SMA practice organisation-specific?
-
Meredith Ltd makes a special-purpose machine D4H used in the textile industry. Meredith has designed the D4H machine for 2008 to be distinct from its competitors. It has been generally regarded as a...
-
Determine the static deflection of the spring in the system of Figure P2.21. E m k FIGURE P 2.21 E, I
-
Determine the static deflections in each of the springs in the system of Figure P2.22. 40 cm 20 cm 1 x 105 N/m 2 x 105 N/m FIGURE P 2.22 4 kg
-
A \(30 \mathrm{~kg}\) compressor sits on four springs, each of stiffness \(1 \times 10^{4} \mathrm{~N} / \mathrm{m}\). What is the static deflection of each spring.
Study smarter with the SolutionInn App