Question

if A=[-3,1] and B=[-2,4], find
AUB
A-B
B-A
A intersection B​

Answer 1

Answer:

Given, A={1,2,3,4,5},B={2,4,6,8} and C={3,4,5,6}

For the LHS:

Union of two sets will have the elements of both sets.

So, B∪C={2,3,4,5,6,8}

A−(B∪C) will have elements of A which are not in (B∪C)

So, A−(B∪C)={1} ..... (1)

For the RHS:

A−B will have elements of A which are not in B.

So, A−B={1,3,5}

A−C will have elements of A which are not in C.

So, A−C={1,2}

Intersection of two sets has the common elements of both the sets.

⇒(A−B)∩(A−C)={1} ..... (2)

From (1) and (2), we have

A−(B∪C)=(A−B)∩(A−C)

Hence, the given expression is true.

Step-by-step explanation:

I hope it helps you

Answer 2

The question given is slightly wrong. Detailed explanation is given below.

If A = [-3 1] and B = [-2 4] find AUB, A-B, B-A, A∩B

Answer:

AUB = {-3,-2,-1,0,1,2,3,4}

 A-B = {-3}

 B-A = {2,3,4}

A∩B =  {-2,-1,0,1}

Step-by-step explanation:

Set:

• An orderly group of components is referred to as a set. Curly braces are typically used to indicate it after a capital letter. In the English alphabet,
• For instance, if we were to say, "Make a set of all the vowels," it would look like this: S = {a,e,i,o,u}
• A set with a fixed or known number of items is said to be finite.

      Given A = [-3 1] and B = [-2 4]

      then A = {-3,-2,-1,0,1}, B = {-2,-1,0,1,2,3,4}

          AUB = {-3,-2,-1,0,1} U {-2,-1,0,1,2,3,4}

                   = {-3,-2,-1,0,1,2,3,4}

            A-B = {-3,-2,-1,0,1} - {-2,-1,0,1,2,3,4}

                   = {-3}

           B-A =  {-2,-1,0,1,2,3,4} - {-3,-2,-1,0,1}

                  = {2,3,4}

          A∩B = {-3,-2,-1,0,1} ∩ {-2,-1,0,1,2,3,4}

                  = {-2,-1,0,1}

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