Understanding Set Theory Complements

complement of a set. A universal set is the set of all the elements involved in the problem under consideration. It is denoted by the uppercase letter U. The complement of set A is the set of all the elements in the universal set that are not in set A. it is the difference of the universal set u and set a the complement of set is denoted by a prime example number one let the universal set contains the elements one two three four five six seven eight and 9. And set A contains the elements 2, 4, 6, and 8. Letter A. Find the complement of set A. Letter B. Illustrate the complement of set A using Venn diagram. Solution for letter A. Let us Examine the elements of the universal set and the elements of set A. If the element is in the universal set but not in set A, let us underline it. If the element is in the universal set and is also in set A, let us encircle it. 1 is in the universal set. It is not in set A. Underline 1. 2 is in the universal set. It is also in set A. And circle 2. 3 is in the universal set. It is not in set A. Underline 3. 4 is in the universal set. It is also in set A. And circle 4. four five is in the universal set it is not in set a underline five six is in the universal set it is also in set a and circle six seven is in the universal set it is not in set a underline seven eight is in the universal set it is also in set A and circle 8. 9 is in the universal set it is not in set A underline 9. the elements 1 3 5 7 and 9 which are underlined are in the universal set but are not in set A Therefore, the complement of set A contains the elements 1, 3, 5, 7, and 9. Letter B. The universal set is represented by a rectangle in the Venn diagram. Let us draw rectangle and then write the uppercase letter U to denote the universal set. Write or copy the elements of the universal set inside the rectangle. 1, 2, 3, 4, 5, 6, 7, 8. And 9. We can see in the problem that all the elements of set A are in the universal set. And when we draw a circle for our Venn diagram, the circle should be within or inside the rectangle. And it should contain the elements 2, 4, 6, and 8. Let us draw a circle and name it A. Shade the complement of set A. The complement of set A is shaded light blue. Example number 2. Let the universal set contains the elements 1, 2, 3, 4, 5, 6, 7, 8, and 9. Set A contains the elements 2, 4, 6, and 8. And set B contains the elements 3, 4, 5, and 6. letter a find the complement of a union b letter b illustrate the complement of a union b using venn diagram solution for letter a first find a union b the union of set a and set b is the set of all the elements which belong to set a or to set b or to both sets so a union b contains the elements two three four five six and eight next inspect the elements of the universal set if the element is in the universal set and is not in a union b underline it If the element is in the universal set and is also in A union B and circle it. 1 is in the universal set. It is not in A union B underline 1. 2 is in the universal set. It is also in A union B and circle 2. 3 is in the universal set. it is also in a union b and circle three four is in the universal set it is also in a union b and circle four five is in the universal set it is also in a union b and circle five six is in the universal set it is also in a union b and circle six seven is in the universal set it is not in a union b underline seven eight is in the universal set it is also in a union b and circle eight nine is in the universal set it is not in a union b underline nine the underlying elements which are 1, 7, and 9, are in the universal set but are not in A union B. Hence, the complement of A union B contains the elements 1, 7, and 9. Letter B. Draw a rectangle to represent the universal set U write or copy the elements of the universal sets inside the rectangle one two three four five six seven eight and nine notice that set A and set B are joint sets with common elements 4 and 6. Also, set A and set B are subsets of the universal set. Therefore, the two circles we will draw for our Venn diagram should be drawn within or inside the rectangle. And the two circles should intersect. Let us draw the circles. Our first circle should contain the elements 2, 4, 6, and 8 of set A. Let us name the circle A. The second circle is for set B. It should contain the elements 3, 4, 5, and 6. the intersection or overlapping part should contain the common elements four and six let us name it circle b then shade the complement of a union b the complement of a union b shaded light Example number 3. Let the universal set contains the elements 1, 2, 3, 4, 5, 6, 7, 8, and 9. Set A contains the elements 2, 4, 6, and 8. And set B contains the elements 3, 4, 5, and 6. Letter A. Find the complement of A intersection B. Letter B. Illustrate the complement of A intersection B using Venn diagram. Solution for letter A. First, find A intersection B. The intersection of set A and set B is the set that contains the elements that are common to set a and set b the common elements are four and six next inspect the elements of the universal set if the element is in the universal set and is not in a intersection b underline it Otherwise, encircle it. 1 is in the universal set. It is not in A intersection B under line 1. 2 is in the universal set. It is not in A intersection B under line 2. 3 is in the universal set. It is not in A intersection B. underline 3 4 is in the universal set it is also in a intersection b and circle 4 5 is in the universal set it is not in a intersection b underline 5 6 is in the universal set it is also in a intersection b And circle 6. 7, 8, and 9 are in the universal set. And they are not in A intersection B. Underline 7, 8, and 9. So the elements 1, 2, 3, 5, 7, 8, and 9. are in the universal set but not in A intersection B. Hence, the complement of A intersection B contains the elements 1, 2, 3, 5, 7, 8, and 9. Letter B. Draw a rectangle to represent the universal set U. Write the elements of the universal set inside the rectangle. 1, 2, 3, 4, 5, 6, 7, 8. and 9. Within the rectangle, draw two intersecting circles. Draw a circle. Name the circle A. Draw the second circle. Name the circle B. Circle A contains the elements 2, 4, 6, and 8. And circle B contains the elements 3, 4, 5, and 6. The intersection or overlapping part contains the common elements 4 and 6. Shade the complement of A intersection B. The complement of A intersection B is shaded light blue. Example number 4. Let the universal set contain the elements. 1, 2, 3, 4, 5, 6, 7, 8, and 9. Set A contains the elements 2, 4, 6, and 8. And set B contains the elements 3, 4, 5, and 6. Letter A. Find the complement of B minus A. Letter B. Illustrate the complement of B minus A using Venn diagram. solution for letter a first find b minus a if the element is in set b and is also in set a let us cross it out 3 is in set b it is not in set a 4 is in set b it is also in set a let us cross out 4 5 is in set B. It is not in set A. 6 is in set B. It is also in set A. Let us cross out 6. So B minus A contains the elements 3 and 5. Let us look at the elements of the universal set. 1 is in the universal set. It is not in B. minus a underline 1 2 is in the universal set it is not in b minus a underline 2 3 is in the universal set it is also in b minus a and circle 3 4 is in the universal set it is not in b minus a underline four five is in the universal set it is also in b minus a and circle five six seven eight and nine are in the universal set and they are not in b minus a so underline six seven eight and nine all the underlying elements are in the universal set but are not in b minus a hence the complement of b minus a contains the elements one two four six seven eight and nine let's go to b let us Draw a rectangle to represent the universal set U. Write the elements of the universal set inside the rectangle. 1, 2, 3, 4, 5, 6, 7, 8, and 9. Since the two sets A and B have common elements which are four and six draw within the rectangle two intersecting circles draw a circle and closing the elements of set a name the circle a draw another circle and closing the elements of set B such that in the intersection are the elements 4 and 6. Name the circle B. Shade the complement of B minus A. The complement of B minus A is shaded light blue.

complement of a set. A universal set is the set of all the elements involved in the problem under consideration. It is denoted by the uppercase letter U.

The complement of set A is the set of all the elements in the universal set that are not in set A. it is the difference of the universal set u and set a the complement of set is denoted by a prime example number one let the universal set contains the elements one two three four five six seven eight and 9. And set A contains the elements 2, 4, 6, and 8. Letter A. Find the complement of set A. Letter B. Illustrate the complement of set A using Venn diagram. Solution for letter A.

Let us Examine the elements of the universal set and the elements of set A. If the element is in the universal set but not in set A, let us underline it. If the element is in the universal set and is also in set A, let us encircle it.

1 is in the universal set. It is not in set A. Underline 1. 2 is in the universal set. It is also in set A. And circle 2. 3 is in the universal set.

It is not in set A. Underline 3. 4 is in the universal set. It is also in set A. And circle 4. four five is in the universal set it is not in set a underline five six is in the universal set it is also in set a and circle six seven is in the universal set it is not in set a underline seven eight is in the universal set it is also in set A and circle 8. 9 is in the universal set it is not in set A underline 9. the elements 1 3 5 7 and 9 which are underlined are in the universal set but are not in set A Therefore, the complement of set A contains the elements 1, 3, 5, 7, and 9. Letter B. The universal set is represented by a rectangle in the Venn diagram. Let us draw rectangle and then write the uppercase letter U to denote the universal set.

Write or copy the elements of the universal set inside the rectangle. 1, 2, 3, 4, 5, 6, 7, 8. And 9. We can see in the problem that all the elements of set A are in the universal set. And when we draw a circle for our Venn diagram, the circle should be within or inside the rectangle.

And it should contain the elements 2, 4, 6, and 8. Let us draw a circle and name it A. Shade the complement of set A. The complement of set A is shaded light blue. Example number 2. Let the universal set contains the elements 1, 2, 3, 4, 5, 6, 7, 8, and 9. Set A contains the elements 2, 4, 6, and 8. And set B contains the elements 3, 4, 5, and 6. letter a find the complement of a union b letter b illustrate the complement of a union b using venn diagram solution for letter a first find a union b the union of set a and set b is the set of all the elements which belong to set a or to set b or to both sets so a union b contains the elements two three four five six and eight next inspect the elements of the universal set if the element is in the universal set and is not in a union b underline it If the element is in the universal set and is also in A union B and circle it.

1 is in the universal set. It is not in A union B underline 1. 2 is in the universal set. It is also in A union B and circle 2. 3 is in the universal set.

it is also in a union b and circle three four is in the universal set it is also in a union b and circle four five is in the universal set it is also in a union b and circle five six is in the universal set it is also in a union b and circle six seven is in the universal set it is not in a union b underline seven eight is in the universal set it is also in a union b and circle eight nine is in the universal set it is not in a union b underline nine the underlying elements which are 1, 7, and 9, are in the universal set but are not in A union B. Hence, the complement of A union B contains the elements 1, 7, and 9. Letter B. Draw a rectangle to represent the universal set U write or copy the elements of the universal sets inside the rectangle one two three four five six seven eight and nine notice that set A and set B are joint sets with common elements 4 and 6. Also, set A and set B are subsets of the universal set. Therefore, the two circles we will draw for our Venn diagram should be drawn within or inside the rectangle.

And the two circles should intersect. Let us draw the circles. Our first circle should contain the elements 2, 4, 6, and 8 of set A.

Let us name the circle A. The second circle is for set B. It should contain the elements 3, 4, 5, and 6. the intersection or overlapping part should contain the common elements four and six let us name it circle b then shade the complement of a union b the complement of a union b shaded light Example number 3. Let the universal set contains the elements 1, 2, 3, 4, 5, 6, 7, 8, and 9. Set A contains the elements 2, 4, 6, and 8. And set B contains the elements 3, 4, 5, and 6. Letter A. Find the complement of A intersection B. Letter B. Illustrate the complement of A intersection B using Venn diagram.

Solution for letter A. First, find A intersection B. The intersection of set A and set B is the set that contains the elements that are common to set a and set b the common elements are four and six next inspect the elements of the universal set if the element is in the universal set and is not in a intersection b underline it Otherwise, encircle it. 1 is in the universal set.

It is not in A intersection B under line 1. 2 is in the universal set. It is not in A intersection B under line 2. 3 is in the universal set. It is not in A intersection B.

underline 3 4 is in the universal set it is also in a intersection b and circle 4 5 is in the universal set it is not in a intersection b underline 5 6 is in the universal set it is also in a intersection b And circle 6. 7, 8, and 9 are in the universal set. And they are not in A intersection B. Underline 7, 8, and 9. So the elements 1, 2, 3, 5, 7, 8, and 9. are in the universal set but not in A intersection B. Hence, the complement of A intersection B contains the elements 1, 2, 3, 5, 7, 8, and 9. Letter B. Draw a rectangle to represent the universal set U. Write the elements of the universal set inside the rectangle.

1, 2, 3, 4, 5, 6, 7, 8. and 9. Within the rectangle, draw two intersecting circles. Draw a circle. Name the circle A.

Draw the second circle. Name the circle B. Circle A contains the elements 2, 4, 6, and 8. And circle B contains the elements 3, 4, 5, and 6. The intersection or overlapping part contains the common elements 4 and 6. Shade the complement of A intersection B.

The complement of A intersection B is shaded light blue. Example number 4. Let the universal set contain the elements. 1, 2, 3, 4, 5, 6, 7, 8, and 9. Set A contains the elements 2, 4, 6, and 8. And set B contains the elements 3, 4, 5, and 6. Letter A. Find the complement of B minus A.

Letter B. Illustrate the complement of B minus A using Venn diagram. solution for letter a first find b minus a if the element is in set b and is also in set a let us cross it out 3 is in set b it is not in set a 4 is in set b it is also in set a let us cross out 4 5 is in set B. It is not in set A. 6 is in set B.

It is also in set A. Let us cross out 6. So B minus A contains the elements 3 and 5. Let us look at the elements of the universal set. 1 is in the universal set. It is not in B. minus a underline 1 2 is in the universal set it is not in b minus a underline 2 3 is in the universal set it is also in b minus a and circle 3 4 is in the universal set it is not in b minus a underline four five is in the universal set it is also in b minus a and circle five six seven eight and nine are in the universal set and they are not in b minus a so underline six seven eight and nine all the underlying elements are in the universal set but are not in b minus a hence the complement of b minus a contains the elements one two four six seven eight and nine let's go to b let us Draw a rectangle to represent the universal set U.

Write the elements of the universal set inside the rectangle. 1, 2, 3, 4, 5, 6, 7, 8, and 9. Since the two sets A and B have common elements which are four and six draw within the rectangle two intersecting circles draw a circle and closing the elements of set a name the circle a draw another circle and closing the elements of set B such that in the intersection are the elements 4 and 6. Name the circle B. Shade the complement of B minus A. The complement of B minus A is shaded light blue.

Transcript for:Understanding Set Theory Complements

Transcript for:
Understanding Set Theory Complements