Question

Can someone help me here please! thankyou​

Answer 1

AUB = {0,1,2,3,4,6,8}

B∩C = Nil

Xc∩Yc = {February, April, August, September, November, December}

(YUZ)c= {February, March, April, May, August}

the symbol c stands for complement in the solution.

Explanation:

union is combining all the elements of sets A and B

AUB = {0,1,2,3,4,6,8}

intersection is combining only the common elements present in both B and C

B∩C = Nil

complement of a set is the number of elements that are not present in the set.

Xc = {January, February, April, August, September, November, December}

Yc= {February, March, April, May, August, September, October, November, December}

Xc∩Yc = {February, April, August, September, November, December}

Y∪Z = {January, June, July, September, October, November, December}

(YUZ)c= {February, March, April, May, August}

the symbol c stands for complement in the solution.

Answer 2

1. A⋃B = {0, 1, 2, 3, 4, 6, 8}
2. B⋂C = { } . . . (the empty set)
3. X'⋂Y' = {Feb, Apr, Aug, Sep, Nov, Dec}
4. (Y⋃Z)' = {Feb, Mar, Apr, May, Aug}

Explanation:

Given various set definitions, you want to find the union and the intersection of specific pairs of sets.

We find it convenient to list the set contents in such a way that we can readily identify elements in one set or another, neither, or both. That is what we have done in the attachment.

1. A⋃B

The union of sets A and B will be the list of elements in either set. That is, if an element is included in set A or in set B, it is included in their union. An element is only listed once, even if it appears in both sets.

A⋃B = {0, 1, 2, 3, 4, 6, 8}

2. B⋂C

The intersection of sets B and C will be the list of elements contained in both sets. Set B is even digits, and set C is odd digits. Since there are no digits that are both even and odd, their intersection is the empty set.

B⋂C = { } . . . (the empty set)

3. X'⋂Y'

The intersection of the complements of sets X and Y is the list of elements of U that are not in either set.

X'⋂Y' = {Feb, Apr, Aug, Sep, Nov, Dec}

4. (Y⋃Z)'

The complement of the union of Y and Z is the list of elements of U that are not in either of sets Y or Z. This is effectively the same as Y'⋂Z'.

(Y⋃Z)' = {Feb, Mar, Apr, May, Aug}

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Additional comment

We have elected to abbreviate the month names for problems 3 and 4. Your answer may need to spell them out completely to match the problem statement.