Draw Venn Diagrams to represent each set. A ∪ ( A ∩ B )

The set ( A ∩ B ) consists of common elements between set A and B. The union of set A with intersection of set A and B would give set A. This is because, common elements of A and B is included in A. Here, U is the universal set represented by rectangle. The circle with slant lines represent set A i.e. the required Set. The portion with criss-cross lines represent ( A ∩ B ) .

Draw Venn Diagrams to represent each set. A ∪ ( A ∩ B )

The set ( A ∩ B ) consists of common elements between set A and B. The union of set A with intersection of set A and B would give set A. This is because, common elements of A and B is included in A. Here, U is the universal set represented by rectangle. The circle with slant lines represent set A i.e. the required Set. The portion with criss-cross lines represent ( A ∩ B ) .

Draw Venn diagrams to represent each set. ( A ' ∩ B ) '

The universal set has been represented with a rectangle. The intersection of complement of A and B has the elements of ( B - A ) as its elements. So, intersection of B and complement of A is ( A ' ∩ B ) . The complement of this set is given by U - ( A ' ∩ B ) . A and B are represented by two circles with names inside. The universal set U is represented by rectangle.

Draw Venn Diagrams to represent each set. ( A ' ∪ B ' ) '

We represent the set A and B by two circles. The universal set is represented as rectangle U.The complement of A is the portion in U outside A. This portion is marked by the space outside the circle A, including part of B. The complement of B is the portion in U outside the circle B. This portion is the white and blank space outside B, including parts of A. The union of complement of A and complement of B is the complement of A intersection B. Thus, { ( A ' ∪ B ' ) ' } is the set A intersection B. This set is marked by slanted lines.

Draw Venn Diagrams to represent each set. A ∪ ( B ∩ C )

To represent the given diagram, it would be convenient to assume three mutually intersecting sets A, B and C. We represent set A with horizontal lines, set B by vertical lines, and set C by dotted lines.The set resulting from the given operation would be equivalent to the union on A with the difference of the intersection of A, B, C and intersection of B, C. The required region is marked by tick sign.

Draw Venn Diagrams to represent each set. A ∩ ( B ∪ C ) '

A Venn diagram is a diagram that helps us visualise the logical relationship between sets and their elements. A Venn diagram typically uses intersecting and non-intersecting circles to denote the relationship between sets. The union of two sets A and B is the set of elements which are in A , in B , or in both A and B . Venn diagram representing B ∪ C is: The complement of set A is defined as a set that contains the elements present in the universal set but not in set A . Venn diagram representing B ∪ C ' is The intersection of a set A and a set B is the set of elements that are in both set A and B . The Venn diagram representing A ∩ ( B ∪ C ) ' is:

Draw Venn Diagrams to represent each set. ( A ∩ B ) ∪ ( A ∩ C ) ∪ ( B ∩ C )

Let us represent the Universal set with the rectangle U. Let us represent the sets A, B and C by three circles within U. The region representing the set resulting from the given operation is given horizontally lined portions.