The Mathematics of Tenure, Car Lights, and Logic Gates

In a state office, an employee maybe tenured if (1) he has passed the Career Service Examination, or (2) he has worked as a probationary employee for more than 10 years.

Notice that the employee maybe tenured if either one of the conditions above is satisfied. He may also be tenured if both conditions are satisfied. If we create a table and rephrase the statements above to question form, we can see that the only reason for an employee not to be tenured is if the answer to both questions is NO.

tenure-table

The first table is also the same as the table shown below.  In the second table,  the situation describes the relationship between a car’s ceiling light and its two doors. Unless the ceiling light is turned on or off manually, it will always be ON if both doors or one of the two doors is open. The only time that the light will be OFF is if the two doors are shut. » Read more

Math, Santa, and Venn Diagrams

It’s nearly Christmas, so I’d like to have some rest and avoid serious math posts. To be honest, I’m really thinking about the costume that I’m going to wear tomorrow for our Any Costume Christmas party. I’m thinking about a Dragon Ball Z costume (Vegeta perhaps?). I suppose we have the same height (lol).

Anyway, I found a Venn diagram (see, it’s still related to math), with Santa on the intersection. You would probably agree with me that the one who thought about this is a genius.

By the way, a Venn diagram is a schematic diagram that show logical relations between sets (sorry can’t help it). Venn diagrams are used in elementary set theory especially to represent set relationships in probability, logic, statistics, and computer science.

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