To save typing, I'll write
Bergman gives in part (a) a list of identities which follow from the defining identities of
For completeness, I'll give proofs of these five identities inside the spoiler blocks.
Ok, now we add the additional defining identity of
Our task is to understand
Recall that every element of the free algebra
Level 0: a, b
Level 1: a, b, aa, ab, ba, and bb.
Note that we can eliminate aa and bb since they are redundant:
Now it turns out that any term at Level 2 (any product of a, b, ab, and ba) can be shown to be equivalent to a term at Level 1, using the identities above. They multiply according to the following Cayley table:
I've hidden the derivations in the spoiler blocks below.
When a cold drink is taken from a refrigerator, its temperature is 5 degree C. After 25 minutes in a 20 degree C room its temperature has increased to 10 degree C. What is the temperature of the drink after 50 minutes?
How many minutes are there in hours?
Find the answer for power .
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B)increase with time;
C)decrease with time;
D)None of these
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How to write in scientific notation?