Step 1:

It is given that universal set is \(A={x \in R|-1<x\ \le0}\)and

\(B={x \in R|0\ \le x<1}\)

a.Obtain the set \(A \cup B\) as follows:

\(A \cup B={x \in R|-1<x\ \le 0}\cup{x \in R|0\ \le x<1}\)

\(={x \in R|-1<x<1}\)

Step 2:

b: Obtain the set \(A \cap B\) as follows

\(A\cap B={x \in R|-1<x\ \le 0}\cap{x \in R|0\ \le x<1}\)

\(={x \in R|x=0}\)

\(=0\)

c.Obrain the set \(A^c\) as follows:

\(A^c=(R\ A)\)

\(=R{x \in R|-1<x\ \le 0}\)

\(=(-oo,-1]\cup(0,\infty)\)