Problem #$1.$ Construct DFAs for the following languages:

The set of all binary strings beginning with $010$ and ending with $101.$

$($Note that the string $0101$ should be accepted.$)$

The set of strings over $\{0,1\}$ which do not contain $0110$ as substring.

The set of strings over $\{a,b\}$ such that the fourth symbol from the right is $a$

The set of all strings $w_{1}dots{w}_n,n0,$ over $\{0,1,2,3,4\}$ such that $w_1+$cdots$+w_n-=$

$0(mod5)$

The set of binary strings containing at least two $1$ s and at most three $0$ s $.$