Modulo Arithmetic

The keys $5,28,19,15,26,33,12,17,10$ are inserted into a hash table using the hash function $h(k)=k \bmod 9$. The collisions are resolved by chaining. After all the keys are insert...

Let Σ = {1,2,3,4}. For x ∈ Σ*, let prod(x) be the product of symbols in x modulo 7. We take prod(ε) = 1, where ε is the null string. For example, prod(124) = (1 × 2 × 4) mod 7 = 1....

Let $\Sigma=\{1,2,3,4\}$ For $x \in \Sigma^*$, let prod $(x)$ be the product of symbols in $x$ modulo 7 . We take $\operatorname{prod}(\varepsilon)=1$, where $\varepsilon$ is the n...

Let Zₙ be the group of integers {0, 1, 2, ..., n-1} with addition modulo n as the group operation. The number of elements in the group Z₂ × Z₃ × Z₄ that are their own inverses is _...

Consider the following language. L = {x $$ \in $$ {a, b}* | number of a’s in x is divisible by 2 but not divisible by 3} The minimum number of states in a DFA that accepts L is ___...

For $$s \in {\left( {0 + 1} \right)^ * },$$ let $$d(s)$$ denote the decimal value of $$s(e. g.d(101)=5)$$ Let $$L = \left\{ {s \in {{\left( {0 + 1} \right)}^ * }\left| {\,d\left( s...

Given the following input (4322, 1334, 1471, 9679, 1989, 6171, 6173, 4199) and the hash function x mod 10, which of the following statements are true? i) 9679, 1989, 4199 hash to t...

The smallest finite automaton which accepts the language $$L = \left. {\left\{ x \right.} \right|$$ length of $$x$$ is divisible by $$\left. 3 \right\}$$ has

Let $$S = \left\{ {0,1,2,3,4,5,6,7} \right\}$$ and $$ \otimes $$ denote multiplication modulo $$8$$, that is, $$x \otimes y = \left( {xy} \right)$$ mod $$8$$ (a) Prove that $$\left...