 Let the universal set the set of R of all real numbers andLet A={x in R|-1<x underset(-)(<)0} & B={x in R|0underset(-)(<)X<1}a:find A cup Bb:Find A cap Bc:Find A^c sagnuhh 2020-11-03 Answered

Let the universal set the set of R of all real numbers and
Let $$A={x \in R|-1<x\ \le 0}\ and\ B={x \in R|0\ \le X<1}$$
a:find $$A \cup B$$
b:Find $$A \cap B$$
c:Find $$A^c$$

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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:
$$A^c=(R\ A)$$
$$=R{x \in R|-1<x\ \le 0}$$
$$=(-oo,-1]\cup(0,\infty)$$