Solving Complex If/Then Statements

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In summary, the conversation is about a logical proof where the rules of inference and replacement are used to reach a conclusion. The final statement B v W is achieved using the rules of conjunction, distribution, simplification, and addition.
  • #1
qwpoi
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This is driving me nuts. I'm sure the answer is completely obvious.

I'm using > for the if A then B b/c there's no keyboard symbol for that, and * for the and operator because same reason.

1. B v (S*N)
2. B > ~S
3. S > ~ N / B v W

I have no idea what to do with these if/then statements, how to separate them, or anything, because I can't get any of the premises by themselves from the first statement.

Please help? Thanks.
 
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  • #2
I have no idea what your question is. Are these three statements the hypotheses and you want to decide what you can prove from them? Are they steps in a proof any you want to decide what you conclude? Is the last step the conclusion and you want to know if the argument is valid? What is it you want to know?
 
  • #3
Sorry, should have explained more. It's a logical proof, and we have so far learned the a bunch of rules of inference and replacement. I had an epiphany in class though that I was forgetting one rule, and so was able to do it.

solution:
1. B v (S*N)
2. B > ~S
3. S > ~ N / B v W
4. (B>~S) * (S>~N) 2, 3 Conj
5. (BvS)*(BvN) 1 dist
6. BvS 5, simp
7. ~Sv~N 4, 6 CD
8. ~(S*N) DM 7
9. (S*N)vB 1 comm
10. B 8, 9 DS
11. BvW add 10
 

FAQ: Solving Complex If/Then Statements

How do I approach solving complex if/then statements?

To solve complex if/then statements, you should first read and understand the problem carefully. Then, identify all the conditions and relationships between them. Next, use logical reasoning to determine the possible outcomes for each condition. Finally, combine these outcomes using logical operators to arrive at the final solution.

What are some common logical operators used in solving if/then statements?

The most common logical operators used in solving if/then statements are AND, OR, and NOT. These operators help to combine multiple conditions and determine the final outcome based on logical rules.

How do I handle nested if/then statements?

Nested if/then statements are used when there are multiple conditions to be evaluated. To handle them, you should first evaluate the innermost condition and then work your way outwards. This will help you break down the problem into smaller, more manageable parts.

What are some strategies for simplifying complex if/then statements?

One strategy for simplifying complex if/then statements is to use truth tables. This involves creating a table with all the possible combinations of conditions and their outcomes. Another strategy is to use De Morgan's laws, which allow you to simplify complex logical expressions by converting them into equivalent forms.

Can I use programming language to solve complex if/then statements?

Yes, programming languages offer built-in functions and methods to handle complex if/then statements. These languages also allow you to create custom functions to handle specific logic and conditions. However, it is important to have a good understanding of logic and logical operators before attempting to solve complex if/then statements using programming languages.

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