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## Main Question or Discussion Point

**Defining OR**

Given set A and B, the union is defined as

[tex]A\cup B := \{x | x \; \epsilon A \lor x \; \epsilon \; B \}[/tex]

But how is [tex]\lor[/tex] defined?

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- Thread starter Swapnil
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- #1

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Given set A and B, the union is defined as

[tex]A\cup B := \{x | x \; \epsilon A \lor x \; \epsilon \; B \}[/tex]

But how is [tex]\lor[/tex] defined?

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- #2

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It's defined as or. As in A v B is the condition that A holds, or B holds, or both hold.

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- #4

verty

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Oh, perhaps this is circular.

- #5

radou

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A | B | A V B

-----------------------------------

T | T | T

T | F | T

F | T | T

F | F | F

-----------------------------------

T | T | T

T | F | T

F | T | T

F | F | F

- #6

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I think this is circular too.

Oh, perhaps this is circular.

Correct me if I am wrong. You define OR as a function [tex]f: (x,y) \to z[/tex] where [tex] x,y,z \; \epsilon \; \{0, 1\}[/tex] satisfying the following property:

[tex](x,y) = (0,0) \Rightarrow z = 0 \land (x,y) \neq (0,0) \Rightarrow z = 1 [/tex]

I guess the circularity of this definition depends on how you define [tex]\land[/tex] and [tex]\Rightarrow[/tex]...

- #7

radou

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What exactly is circular in the definition?

- #8

cristo

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Given set A and B, the union is defined as

[tex]A\cup B := \{x | x \; \epsilon A \lor x \; \epsilon \; B \}[/tex]

But how is [tex]\lor[/tex] defined?

This is not a definition of "A or B"; it is a definition of the union of the sets A and B. This is not a circular definition.ORB as true when either A is trueORB is trueORboth are true!

- #9

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Well... nothing yet. Until you start defining [tex]\land[/tex] and [tex]\Rightarrow[/tex]What exactly is circular in the definition?

Notice that

[tex] p \Rightarrow q : = \lnot p \lor q[/tex]

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- #10

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I was actually talking about the definition of OR as mentioned by DeadWolfe.This is not a definition of "A or B"; it is a definition of the union of the sets A and B. This is not a circular definition.

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cristo

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Sorry, I read the post incorrectlyI was actually talking about the definition of OR as mentioned by DeadWolfe.

- #12

matt grime

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There is nothing at all 'circular' in any of these definitions. It would have been better written as

(x in A)v(x in B)

to avoid confusion (his A and B are not your A and B). What on earth do you think the definition of logical OR is if not what was given? V is just another symbol for logical OR.

Do'nt confuse sets with conditions that define the sets: the defining condition for a union of two sets is the disjunction (OR) of the individual conditions.

(x in A)v(x in B)

to avoid confusion (his A and B are not your A and B). What on earth do you think the definition of logical OR is if not what was given? V is just another symbol for logical OR.

Do'nt confuse sets with conditions that define the sets: the defining condition for a union of two sets is the disjunction (OR) of the individual conditions.

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- #14

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But they are the same thing! Call it 'V', or 'OR' or 'or.' It is still a logical OR.

Anyways, say that you do define v to be or. The how do you then define or?

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I know that. I am just asking how the disjunction (OR) is defined. (I guess I should have never brought sets in my question. And my title was a big mistake too. ).What on earth do you think the definition of logical OR is if not what was given? V is just another symbol for logical OR.

Do'nt confuse sets with conditions that define the sets: the defining condition for a union of two sets is the disjunction (OR) of the individual conditions.

- #16

matt grime

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