Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Let * be a binary logical connective that makes (P*Q)^(Q*P) logically equivalent to PQ. Show that..... if in addition P * Q is not always

image text in transcribed

Let * be a binary logical connective that makes (P*Q)^(Q*P) logically equivalent to PQ. Show that.....

if in addition P * Q is not always true, then * is 2.37 Remark. Let * be a binary logical connective. In Theorem 2.17, we saw that (P Q)A(Q > P) is logically equivalent to PQ. Similarly, it is easy to see that (PQ) / (Q P) is logically equivalent to P Q. Finally, it should be obvious that (P Q) (QP) is logically equivalent to P Q. Thus ly equivalent to P# Q. In part (a) if * is or if * is +., or if * is , then (P * Q) ^ (Q * P) is logical of the next exercise, you are asked to prove the converse of this. Exercise 34. Let * be a binary logical connective that makes (L, Q)A (Q * P logically equivalent to (a) Show that * is , or * is , or * is. In other words, show that the truth table for * is the same as the truth table for or the truth table for ., or the truth table for f. (Warning: In my experience, many students do not solve this exercise correctly. Instead, they prove the converse of what is asked. In other words, they just reprove the facts that are pointed out in Remark 2.37 Then figure out as much as you can about T F and F * T.) (b) Now suppose in addition that * makes (RAS) *R a tautology. Show that then * is . In other words, show that the truth table for * is the same as the truth table for . (The warning for part (a) applies here too. Hint: Combine part (a) of this exercise with Example 2.35(a))

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

The Structure Of The Relational Database Model

Authors: Jan Paredaens ,Paul De Bra ,Marc Gyssens ,Dirk Van Gucht

1st Edition

3642699588, 978-3642699580

More Books

Students also viewed these Databases questions