Confused about logical statements.

  • Thread starter torquerotates
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In summary, the conversation is discussing the use of logical operators, specifically the "or" operator. The question is raised whether the statement "A and B or C" makes sense, as logical operators are typically binary. It is clarified that the "or" links to C, but it is unclear what is on the other side. The conversation then delves into the concept of distributive law in arithmetic and how it relates to logical operators. It is concluded that the use of parentheses is necessary to ensure clarity in interpreting the statement.
  • #1
torquerotates
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A and B or C


Does that even makes sense as a statement?
I thought logical operators are binary.

Obviously, the "or" links to C but what is on the other side? A or B?

i mean 1+2-3=0 makes sense since (1+2)-3=3-3=0=1-1=1+(2-3)

But [(A and B) or C]=(AorC)and(BorC)
[ A and ( B or C) ]= (AandB)or(AandC)

these are not the same.
 
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  • #2
Your analogy is incorrect. The corresponding expression in arithmetic would involve both multiplication and addition (distributive law). a(b+c) = ab + ac.
 
  • #3
torquerotates said:
A and B or C

You really need to use parentheses to be clear


I think most computer languages will interpret it as

(A and B) or C

But I know of at least one that will make it

A and (B or C)
 

1. What is a logical statement?

A logical statement is a declarative sentence that can be either true or false. It is composed of one or more propositions or statements that are connected by logical operators such as "and", "or", and "not".

2. How do you determine the truth value of a logical statement?

The truth value of a logical statement is determined by evaluating each proposition separately and then combining them using the logical operators. If all propositions are true, the statement is true. If one or more propositions are false, the statement is false.

3. What are the different types of logical statements?

The main types of logical statements are conjunctions (and), disjunctions (or), negations (not), and conditionals (if-then). These can be further categorized into compound statements, which combine two or more simple statements, and complex statements, which contain nested logical statements.

4. How do I use logical statements in scientific research?

Logical statements are commonly used in scientific research to formulate hypotheses, make predictions, and draw conclusions. They are also used in experimental design, data analysis, and building mathematical models to explain natural phenomena.

5. Can a logical statement be both true and false?

No, a logical statement cannot be both true and false at the same time. This would violate the law of non-contradiction, which states that something cannot both be and not be at the same time. However, a statement can be undetermined or indeterminate if the truth value cannot be determined due to incomplete or conflicting information.

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