Simple Discrete Structures problem

W-->S)^(S-->W).In summary, the conversation is about the first assignment in a class that involves negating and simplifying a logical structure with the bi-conditional implication W <--> S. The conversation includes a step-by-step process of how to arrive at the simplified negation of (W --> S) ^ (S --> W). This involves using DeMorgan's Law and simplifying implications. The end result is equivalent to W (XOR) S. The use of "~" in front of the implications is to signify negation.
  • #1
Firestrider
104
0
OK this is the first assignment I have in this class and I can't figure out how to negate and simplify the logical structure of W <--> S (bi-conditional implication)

I got this so far:

~[(W --> S) ^ (S --> W)] by Definition
~(W --> S) v ~(S --> W) by DeMorgan's Law
~(~W v S) v ~(~S v W) by Simplification of Implication

I just don't know where to go to from here. I know the end result would make W <--> S equivalent to W (XOR) S.
 
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  • #2
Why the "~"? I would start with (W--> S)^(S-->W).

Now remember that A-->B is the same as Bv(~A).
 
  • #3
Well the problem says to find the simplified negation, so I thought that meant to negate then simplify. So I negated the whole thing with ~
 

Related to Simple Discrete Structures problem

1. What is a simple discrete structures problem?

A simple discrete structures problem is a problem in mathematics or computer science that involves discrete objects or values, such as integers, graphs, or logical statements. These problems often involve finding patterns or relationships between these objects or values.

2. How are simple discrete structures problems solved?

Simple discrete structures problems are typically solved using mathematical or logical techniques, such as induction, combinatorics, or graph theory. Computer algorithms can also be used to solve these problems efficiently.

3. What are some common applications of simple discrete structures problems?

Simple discrete structures problems have many real-world applications, including cryptography, network routing, and data compression. They are also used in computer science to design efficient algorithms and data structures.

4. Can anyone solve a simple discrete structures problem?

Yes, anyone with a basic understanding of mathematics and logic can solve simple discrete structures problems. However, more complex problems may require specialized knowledge and skills in mathematics or computer science.

5. How do simple discrete structures problems relate to other branches of science?

Simple discrete structures problems are closely related to other branches of science, such as physics, biology, and social sciences. Many scientific theories and models involve discrete objects and values, and simple discrete structures problems can be used to analyze and understand these systems.

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