# LOGIC: if A then B is true

#### 1Thess521

##### Well-known member
It has been decades since I ace’d my class in symbolic logic:

Can you help me with this logical argument?

If A exists then B exists is true
Then not-B must mean not- A is true
However, not-A does not mean not -B

Is that reasoning valid?
Can it be cleaned up?
What is the name of this argument?

It has been decades since I ace’d my class in symbolic logic:

Can you help me with this logical argument?

If A exists then B exists is true
Then not-B must mean not- A is true
However, not-A does not mean not -B

Is that reasoning valid?
Can it be cleaned up?
What is the name of this argument?
The reasoning is valid. The statement can be restated as If A then B, or alternatively A only if B. It can also be represented in a Venn diagram with every instance of B as a circle completely enclosing every instance of A but including instances of B that do not include A. I can't remember the name of the argument, or even if it has a name.

The reasoning is valid. The statement can be restated as If A then B, or alternatively A only if B. It can also be represented in a Venn diagram with every instance of B as a circle completely enclosing every instance of A but including instances of B that do not include A. I can't remember the name of the argument, or even if it has a name.
thanks

does this seem to be the same thing?

thanks

does this seem to be the same thing?
Yes, but frankly the OP is rather more clear.

It has been decades since I ace’d my class in symbolic logic:

Can you help me with this logical argument?

If A exists then B exists is true
Then not-B must mean not- A is true
However, not-A does not mean not -B

Is that reasoning valid?
Can it be cleaned up?
What is the name of this argument?

It's basically a logical conditional with a logical biconditional framework.

This is a logical conditional statement:
(p). If you're in Boston, then you're in Massachusetts.

But this statement is not a logical biconditional:
(q). If you're in Massachusetts, then you're in Boston.

It doesn't have the same truth value. The letter (q) is false because being in Massachusetts doesn't necessitates that you're in Boston. You could be anywhere else in Massachusetts, like Salem or Everett.

Now Contra (against, demonstrating the 'opposite contrast' as equal to contradiction) is clearly understood as "reverse and negate both," or the logical form x ---> y is a contrary to (~y ---> ~x). In other words, the antecedent and consequent are inverted in a negation.

⦁ Modus Tollens (MT): Y ---> X, ~X |- ~Y

It's basically a logical conditional with a logical biconditional framework.

This is a logical conditional statement:
(p). If you're in Boston, then you're in Massachusetts.

But this statement is not a logical biconditional:
(q). If you're in Massachusetts, then you're in Boston.

It doesn't have the same truth value. The letter (q) is false because being in Massachusetts doesn't necessitates that you're in Boston. You could be anywhere else in Massachusetts, like Salem or Everett.

Now Contra (against, demonstrating the 'opposite contrast' as equal to contradiction) is clearly understood as "reverse and negate both," or the logical form x ---> y is a contrary to (~y ---> ~x). In other words, the antecedent and consequent are inverted in a negation.

⦁ Modus Tollens (MT): Y ---> X, ~X |- ~Y

Good example, @Binyawmene, even I could follow along.