Question

Let A = {all real numbers between 0 and 2} and B = {all real numbers less than 1}. Describe the following sets using interval notation. a) A - B b) B - A c) A⊕B d) B ⊕ A Show that A⊕B = (A - B) U (B - A)

          Let A = {all real numbers between 0 and 2} and B = {all real numbers less than 1}. Describe the following sets using interval notation.
a) A - B
b) B - A
c) A⊕B
d) B ⊕ A
Show that A⊕B = (A - B) U (B - A)

Added by Kristen R.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Supreeta N

03/30/2023

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In interval notation, this is represented as: $$[1, 2)$$ Show more…

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Let A = {all real numbers between 0 and 2} and B = {all real numbers less than 1}. Describe the following sets using interval notation. a) A - B b) B - A c) A⊕B d) B ⊕ A Show that A⊕B = (A - B) U (B - A)

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Transcript

00:01 Hi, from the question given that set a contains all real number between 0 to 2.

00:10 So all real number between 0 to 2.

00:19 So set a contains 0 comma 2.

00:26 Interval notation will be 0 comma 2 because all real number between 0 to 2.

00:31 So here we use the open intervals in 0 and 2 or not.

00:35 Included.

00:37 Now set b contained set of all real number that is less than one.

00:43 Real number less than 1.

00:47 So, b will be equal to interval notation minus infinity to 1.

00:57 Now, in part a we need to find a minus b.

01:03 So, a is, let us consider a number line.

01:08 So, a is from 0 to 2.

01:12 And b is from negative infinity to positive 1.

01:19 So here we need to subtract.

01:24 So here we need to subtract this portion but here it is a open interval.

01:30 So the rest of the portion included 1.

01:34 Therefore a minus b is closed interval 1 to 2.

01:39 2 is open interval.

01:41 Now let us move on to b.

01:43 So, for b, we need to find b minus a.

01:47 So, again, let us consider a number line...

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