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Logic introdction

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Logic works like arithmetic.

We can use constants. Those are objects with fix states. With arithmetic we can have 1, 3,19, 34398980923434 but in logic there is only TRUE and FALSE.

We can use variables. Like with arithmetic we often use letters to name them. Their only stats are TRUE and FALSE again. We call this kind of variables booleans. They are named after the mathematician George Boole. a TRUE state is usualy represented with a 1 and a FALSE with a 0.

There is operators. Not all operators are used in all paradigms. The one that are sometimes missing can be made out of those that are there. I will list all of them here and give the truth table associated with it.

BUFFER (or just the name of the input variable)

It is a dirrect link.

exemple: The wall is blue cause the paint used is blue.

a|out

0|0

1|1

NOT

It is a dirrect oposition.

exemple: This card is not the first of spades cause this one is.

a|out

0|1

1|0

AND

This one is true only if all the variables are true.

exemple: I can drive cause I have the key and the car.

a|b|out

0|0|0

0|1|0

1|0|0

1|1|1

OR

This one is true if one of the variables is true.

exemple: I will be happy if I have ice cream or if I have a lipstick.

a|b|out

0|0|0

0|1|1

1|0|1

1|1|1

XOR (exclusive or)

This one is true if one variable is true but false if both are true.

exemple: I will be happy if my mom or my dad gives me that book. But if they both do that. I will be mad that they didn't talk before buying the same thing.

a|b|out

0|0|0

0|1|1

1|0|1

1|1|0

The rest are just negations of the ones above. They are equal to not(f(a, b))

NAND (not and)

a|b|out

0|0|1

0|1|1

1|0|1

1|1|0

NOR (not or)

a|b|out

0|0|1

0|1|0

1|0|0

1|1|0

NXOR (not exclusive or)

Also called imply in boolean logic.

a|b|out

0|0|1

0|1|0

1|0|0

1|1|1

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