Unit 3-Lecture3: Counting with Bijections

1 Counting One Thing by Counting Another

The Bijection Rule： if you figure out the size of one set, then you can immediately determine the sizes of many other sets via bijections.

2 Counting Sequences

Product Rule:
If P1,P2,P3...Pnare finite sets, then:

|P1×P2×P3...×Pn|=|P1|∙|P2|∙...|Pn|

Sum Rule:
If S1,S2,S3...Snare disjoint sets, then:

|S1∪S2∪S3...∪Sn|=|S1|+|S2|+...|Sn|

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Reference

[1] Lehman E, Leighton F H, Meyer A R. Mathematics for Computer Science[J]. 2015.