For 7.23 start by figuring out how many elements you have in each of the sets. Clearly $A$ has $5$ elements. How about $B$? (That is, how many subsets does $A$ have?). Now, to have an injection from $A$ to $B$, you need to assign to each element of $A$ a different element of $B$. In how many ways can this be done?

For a hint on 7.24 check out the post below this.

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