Question

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

Discrete math
ANSWERED
asked 2020-11-03

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

Answers (1)

2020-11-04

Step 1:
It is given that universal set is \(A={x \in R|-1<x\ underset(-)(<)0}\)and
\(B={x \in R|0\ underset(-)(<)x<1}\)
a.Obtain the set \(A \cup B\) as follows:
\(A \cup B={x \in R|-1<x\ underset(-)(<)0}\cup{x \in R|0\ underset(-)(<)x<1}\)
\(={x \in R|-1<x<1}\)
Step 2:
b: Obtain the set \(A \cap B\) as follows
\(A\cap B={x \in R|-1<x\ underset(-)(<)0}\cap{x \in R|0\ underset(-)(<)x<1}\)
\(={x \in R|x=0}\)
\(=0\)

c.Obrain the set \(A^c\) as follows:
\(A^c=(R\ A)\)
\(=R{x \in R|-1<x\ underset(-)(<)0}\)
\(=(-oo,-1]\cup(0,\infty)\)

0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...