Given A = {5, 6, 7}, B = {3, 4, 5, 6}, and C = { 4, 5, 6, 7}. Evaluate each set
A �¿ B
b) A U C
c) B U C
d) (A U B) �¿ C
e) A U (B U C)
f) (A �¿ B) �¿ C
g) (A �¿ B) U C
a) A �¿ B: Well, to evaluate this, we need to find the intersection of sets A and B. And intersecting them would be like making them have a little meet and greet. So, A �¿ B would be the set {5, 6} because 5 and 6 are the only numbers that can show up to this intersection party.
b) A U C: Ah, the union of A and C. It's like combining the groups of friends you have, but without any drama. So, A U C would be the set {4, 5, 6, 7}, because at this gathering, everyone is invited.
c) B U C: Here, we're blending the elements of B and C together. It's like mixing mangoes and pineapples to make a fruit salad. So, B U C would give us the set {3, 4, 5, 6, 7}, but no pineapples, sorry!
d) (A U B) �¿ C: Alright, let's start by merging A and B. It's like mashing potatoes and carrots to make a veggie medley. So, A U B would be {3, 4, 5, 6, 7}, but still no pineapples! Now, let's find the intersection with C. Ah, okay, so the set would be {4, 5, 6, 7}, but without the carrots!
e) A U (B U C): Here, we have a set sandwich! First, let's figure out B U C. It's like combining a burger and a hot dog to make a mega-snack. So, B U C is {3, 4, 5, 6, 7}, but without pickles and onions. Now, let's add A to the mix. The final set would be {3, 4, 5, 6, 7}, basically a delicious monster combo of all the numbers we've got!
f) (A �¿ B) �¿ C: Okay, first, let's find A �¿ B, which is {5, 6} because those are the only numbers attending this party. Now, let's intersect the result with C. Unfortunately, none of the numbers in {5, 6} are available for this intersection, so we end up with an empty set. Sorry, no guests allowed!
g) (A �¿ B) U C: First, let's find A �¿ B, which is {5, 6}, the only numbers having a good time together. Now, let's combine them with C. The final set would be {4, 5, 6, 7}, since everyone was in the mood for a great party, except for those sneaky carrots!
To evaluate each set, we need to perform the corresponding set operations. Let's go step-by-step:
a) A �¿ B (Set difference between A and B):
To find the set difference between A and B, we need to remove any elements in A that are also present in B.
A = {5, 6, 7}
B = {3, 4, 5, 6}
A �¿ B = {7}
b) A U C (Union of A and C):
The union of A and C is the set that contains all elements present in either set A or set C, or in both.
A = {5, 6, 7}
C = {4, 5, 6, 7}
A U C = {4, 5, 6, 7}
c) B U C (Union of B and C):
Similar to the previous step, the union of B and C is the set that contains all elements present in either set B or set C, or in both.
B = {3, 4, 5, 6}
C = {4, 5, 6, 7}
B U C = {3, 4, 5, 6, 7}
d) (A U B) �¿ C (Set difference between the union of A and B and C):
First, we need to find the union of sets A and B and then find the set difference between this union and set C.
A = {5, 6, 7}
B = {3, 4, 5, 6}
C = {4, 5, 6, 7}
(A U B) = {3, 4, 5, 6, 7}
(A U B) �¿ C = {3}
e) A U (B U C) (Union of A and the union of B and C):
First, we need to find the union of sets B and C and then find the union of set A with this union.
A = {5, 6, 7}
B = {3, 4, 5, 6}
C = {4, 5, 6, 7}
(B U C) = {3, 4, 5, 6, 7}
A U (B U C) = {3, 4, 5, 6, 7}
f) (A �¿ B) �¿ C (Set difference between the set difference of A and B and C):
First, we need to find the set difference between A and B, then find the set difference between this result and set C.
A = {5, 6, 7}
B = {3, 4, 5, 6}
C = {4, 5, 6, 7}
(A �¿ B) = {7}
(A �¿ B) �¿ C = {} (Empty set)
g) (A �¿ B) U C (Union of the set difference of A and B and C):
First, we need to find the set difference between A and B, then find the union of this result with set C.
A = {5, 6, 7}
B = {3, 4, 5, 6}
C = {4, 5, 6, 7}
(A �¿ B) = {7}
(A �¿ B) U C = {4, 5, 6, 7}
I hope this helps! Let me know if you have any further questions.
To evaluate each set, we need to understand a few set operations.
1. Union (U): The union of two sets A and B, denoted by A U B, is the set that contains all the elements which are either in set A or in set B, or in both.
2. Intersection (�¿): The intersection of two sets A and B, denoted by A �¿ B, is the set that contains all the elements which are common to both set A and set B.
3. Difference (�¿): The difference between two sets A and B, denoted by A �¿ B, is the set that contains all the elements of set A which are not in set B.
Now, let's evaluate each set:
a) A �¿ B:
Find the common elements between set A and set B. In this case, the common element is 5.
So, A �¿ B = {5}.
b) A U C:
Combine all the elements from set A and set C.
A U C = {5, 6, 7}.
c) B U C:
Combine all the elements from set B and set C.
B U C = {3, 4, 5, 6, 7}.
d) (A U B) �¿ C:
First, find the union of set A and set B.
A U B = {3, 4, 5, 6}.
Then, find the difference between this union and set C.
(A U B) �¿ C = {3}.
e) A U (B U C):
First, find the union of set B and set C.
B U C = {3, 4, 5, 6, 7}.
Then, find the union of set A and the union of set B and set C.
A U (B U C) = {5, 6, 7}.
f) (A �¿ B) �¿ C:
First, find the difference between set A and set B.
A �¿ B = {} (empty set since set A does not have any elements that are not in set B).
Then, find the difference between this empty set and set C.
(A �¿ B) �¿ C = {} (empty set).
g) (A �¿ B) U C:
First, find the difference between set A and set B.
A �¿ B = {} (empty set).
Then, find the union of this empty set and set C.
(A �¿ B) U C = {4, 5, 6, 7}.