Problem $5$

Write $T$ or $F$ for each of the following statements to indicate whether the statement is true or false,

respectively. If the statement is correct, briefly state why. If the statement is wrong, explain why.

Part a

Using division method mode $3,$ three of the following numbers will be hashed to the same slot: $\{1,2,$cdots,$20\}.$

Part b

The hash family $H=\{h_1,h_2,h_3,h_4\}$ is universal, where $h_1,h_2,h_3,h_4$:$\{1,2,3,4,5\}\{0,1,2,3\}$ are

defined by the following table: