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Table of Contents
What is a
Logical Proposition
True Value
and
NOT
AND and OR
XOR
IMP
EQV
Logical Formula
and
Calculation Order
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When one new proposition is made by connecting two propositions, AND and OR are often used. When propositions such as "the flower is red" and "the fruit is sweet" are joined with AND, it becomes "the flower is red" AND "the fruit is sweet." This has the same meaning as "the flower is red and its fruit is sweet." In the same way, "the flower is red" OR "the fruit is sweet" has the same meaning as "the flower is red or its fruit is sweet." Accordingly, for AND and OR, the truth value list can be considered in the same way as NOT.
As shown below, two old predicates can be connected in four different ways.
| A | B | A AND B | A OR B |
| F | F | F | F |
| F | T | F | T |
| T | F | F | T |
| T | T | T | T |
When using AND, two old propositions have to be true or the new proposition will not be true. However, note that for OR, one of the propositions has to be true for the new proposition to be true. The following formulas can be constructed:
| F | AND | F = F |
| F | AND | T = F |
| T | AND | F = F |
| T | AND | T = T |
| F | OR | F = F |
| F | OR | T = T |
| T | OR | F = T |
| T | OR | T = T |
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