Answer
Verified
405.9k+ views
Hint: Here, we will find the set obtained by each of the given expressions and check whether they hold true or not. The intersection of two sets gives the common element present in them and the union of two sets gives all the elements present in the two sets.
Complete step-by-step answer:
A set is a well defined collection of distinct objects, considered as an object in its own right. The union of a collection of a set is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. 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. It is denoted as $A\cup B$. The intersection of two sets A and B denoted by $A\cap B$ is the set containing all elements of A that also belong to B or equivalently, all elements of B that also belong to A. So, x is said to be an element of this intersection $A\cap B$ if and only if x is an element of both A and B.
Here, we are given that:
A = {a, b, c, d, e}
B = {a, c, e, g}
C= {b, e, f, g}
(i) $A\cup B=B\cup A$
The LHS is:
$A\cup B$ = {a, b, c, d, e, g}
The RHS of the equation is:
$B\cup A$ = {a, c, e, g, b, d}
So, we can see that $A\cup B=B\cup A$.
(ii) $A\cup C=C\cup A$
The LHS of the equation is:
$A\cup C$ ={a, b, c, d, e, f, g}
The RHS of the equation is:
$A\cup C$={ a, b, c, d, e, f, g}
So, we can see that $A\cup C=C\cup A$.
(iii) $B\cup C=C\cup B$
The LHS of the equation is:
$B\cup C$ ={a, c, e, g, b, f}
The RHS of the equation is:
$C\cup B$={ b, e, f, g, a, c}
So, we can see that $B\cup C=C\cup B$.
(iv) $A\cap B=B\cap A$
The LHS of the equation is:
$A\cap B$ ={a, c, e}
The RHS of the equation is:
$B\cap A$={ a, c, e}
So, we can see that $A\cap B=B\cap A$.
(v) $B\cap C=C\cap B$
The LHS of the equation is:
$B\cap C$ ={ e, g}
The RHS of the equation is:
$C\cap B$={ e, g}
So, we can see that $B\cap C=C\cap B$.
(vi) $A\cap C=C\cap A$
The LHS of the equation is:
$A\cap C$ ={ b, e}
The RHS of the equation is:
$C\cap A$={ b, e }
So, we can see that $A\cap C=C\cap A$.
Hence, all the conditions are verified.
Note: Students should note that if an element is present in both the sets of which we are taking union, that element will appear only once in their union. Two sets are said to be equal if and only if all the elements are the same.
Complete step-by-step answer:
A set is a well defined collection of distinct objects, considered as an object in its own right. The union of a collection of a set is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. 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. It is denoted as $A\cup B$. The intersection of two sets A and B denoted by $A\cap B$ is the set containing all elements of A that also belong to B or equivalently, all elements of B that also belong to A. So, x is said to be an element of this intersection $A\cap B$ if and only if x is an element of both A and B.
Here, we are given that:
A = {a, b, c, d, e}
B = {a, c, e, g}
C= {b, e, f, g}
(i) $A\cup B=B\cup A$
The LHS is:
$A\cup B$ = {a, b, c, d, e, g}
The RHS of the equation is:
$B\cup A$ = {a, c, e, g, b, d}
So, we can see that $A\cup B=B\cup A$.
(ii) $A\cup C=C\cup A$
The LHS of the equation is:
$A\cup C$ ={a, b, c, d, e, f, g}
The RHS of the equation is:
$A\cup C$={ a, b, c, d, e, f, g}
So, we can see that $A\cup C=C\cup A$.
(iii) $B\cup C=C\cup B$
The LHS of the equation is:
$B\cup C$ ={a, c, e, g, b, f}
The RHS of the equation is:
$C\cup B$={ b, e, f, g, a, c}
So, we can see that $B\cup C=C\cup B$.
(iv) $A\cap B=B\cap A$
The LHS of the equation is:
$A\cap B$ ={a, c, e}
The RHS of the equation is:
$B\cap A$={ a, c, e}
So, we can see that $A\cap B=B\cap A$.
(v) $B\cap C=C\cap B$
The LHS of the equation is:
$B\cap C$ ={ e, g}
The RHS of the equation is:
$C\cap B$={ e, g}
So, we can see that $B\cap C=C\cap B$.
(vi) $A\cap C=C\cap A$
The LHS of the equation is:
$A\cap C$ ={ b, e}
The RHS of the equation is:
$C\cap A$={ b, e }
So, we can see that $A\cap C=C\cap A$.
Hence, all the conditions are verified.
Note: Students should note that if an element is present in both the sets of which we are taking union, that element will appear only once in their union. Two sets are said to be equal if and only if all the elements are the same.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE