I having problems understanding venn set and venn diagrams. Can someone explain this to me.
For the universal set U= {0,1,2,3,4,5,6,7}
And the sets A={1,5}, B={1,2,3,4}
And C= {4, 6} lists the elements in the following
Sets.
a. A�¿B
b. A U B�f
c. A �¿(B U C)
d. C �¿(B �¿ A)�f
Sure, I'd be happy to explain Venn sets and Venn diagrams to you.
Venn sets, also known as Venn diagrams, are graphical representations that show the relationships between different sets or groups of items. They are often used to visualize and understand set operations, such as union, intersection, and complement. Each set is represented by a circle, and the overlapping regions indicate the elements that are common to two or more sets.
Let's analyze the given sets and answer the questions one by one:
For the universal set U = {0,1,2,3,4,5,6,7},
and the sets A = {1,5}, B = {1,2,3,4}, and C = {4,6}:
a. To find ĀB (complement of B with respect to A):
ĀB refers to the elements that are in A but not in B.
In this case, ĀB = {5}.
b. To find A U B̄ (union of A and the complement of B):
A U B̄ refers to the elements that are in either A or in the complement of B (but not in both).
The complement of B with respect to U (universal set) is B̄ = {0,5,6,7} (elements not in B).
Therefore, A U B̄ = {0,1,2,3,4,5,6,7} (all elements from A and B̄).
c. To find Ā(B U C) (complement of the union of B and C with respect to A):
B U C refers to the elements that are in either B or C.
The union of B and C is {1,2,3,4,6}.
Ā(B U C) refers to the elements that are in A but not in (B U C).
In this case, Ā(B U C) = {} (an empty set because all elements of A are present in the union of B and C).
d. To find C̄(B̄Ā) (complement of the intersection of B̄ and Ā with respect to C):
B̄Ā refers to the intersection of the complements of B and A (elements not in B and not in A).
The complement of B with respect to U (universal set) is B̄ = {0,5,6,7}.
The complement of A with respect to U (universal set) is Ā = {0,2,3,4,6,7}.
B̄Ā refers to the elements that are in both B̄ and Ā, which in this case is {0,6,7}.
C̄(B̄Ā) refers to the elements that are in C but not in (B̄Ā).
In this case, C̄(B̄Ā) = {} (an empty set because all elements of C are in the intersection of B̄ and Ā).
I hope this explanation clarifies how to find the elements in the given sets using set operations and Venn diagrams. Let me know if you have any further questions!