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 Question from rashdin, a student: Can you find a set A, |A|=4 and define a bijective function between A and P(A)?

Hi,

Suppose that the elements of $A$ are $a, b, c, \mbox{ and }d.$ Thus $A = \{a, b, c, d\}.$ Can you list the elements of the power set of $A$, $P(A)?$

There is 1 subset of $A$ with 0 elements, the empty set $\emptyset.$

How many subsets are there with 1 element? $\{a\}, \{b\}, \cdot\cdot\cdot$

What about subsets with 2 elements? Three elements? Four elements?

How many is that in total? Can you have a bijection between $A,$ a set with 4 elements and this set?

Penny

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