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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Expert Answer

Clara Reese
Answered 2020-11-04 Author has 16029 answers

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

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