Question

ANSWER THIS QUESTION ILL MARK YOU AS A BRAINLIST ITS URGENT PLEASE​

Answer 1

Answers :-

$\{\}\\\{1,2,3,4,5,6,7,8\}$

Topic :-

Sets and relations

Given:-

• X={ 1, 2, 3, 4}
• Y = {3, 4, 5, 6}
• Z = { 5, 6, 7 , 8}

To find :-

$(X \cap Y )\cap Z$

$(X \cup Y)\cup Z$

SOLUTION:-

$(X \cap Y )\cap Z$

$\bigg(\{1,2,3,4\}\cap\{3,4,5,6\}\bigg)\cap\{5,6,7,8\}$

$\{3,4\}\cap\{5,6,7,8\}$

Since there is no common elements in both sets so the intersection is pie or empty set

So,

$(X \cap Y )\cap Z = \{\}$

Now,

$(X \cup Y)\cup Z$  

$\bigg(\{1,2,3,4\}\cup \{3,4,5,6\}\bigg)\cup\{5,6,7,8\}$

$\{1,2,3,4,5,6\} \cup \{5,6,7,8\}$

$\{1,2,3,4,5,6,7,8\}$

So,

$(X \cup Y)\cup Z= \{1,2,3,4,5,6,7,8\}$

Know more explanation :-

If A,B were given two sets then intersection will be the common elements in both sets

Intersection is represented by the symbol  ∩

If A,B were given two sets then union will be the total elements of both sets.

Union is represented by the symbol  ∪

Know more examples :-

Eg :-

A = {7, 8 , 9 , 10}

B = {9, 10, 11 , 12 , 13}

A∩ B = {9, 10} i.e these elements are present in both sets i.e called as common elements

Eg :-

A = {1,2, 3, 4}

B = {9,10,11 }

A U B = { 1, 2,3 4, 9 , 10 ,11 } i.e both elements of A, B are present