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In a class 35 students, 24 like to play Cricket and 16 like to play Football. Also, each student likes to play a least one of two games. How many students like to play both games?
If \(z\) denotes the set of all integers and \(A = \{ (a,b):{a^2} + 3{b^2} = 28,a,b \in z\} \) and \(B = \{ (a,b):a > b,a,b \in z\} \), then the number of elements in \(A \cap B\) is
And
Let Universal set, \(U = \{ x:{x^5} – 6{x^4} + 11{x^3} – 6{x^2} = 0\} ,\) \(A = \{ x:{x^2} – 5x + 6 = 0\} \& B = \{ x:{x^2} – 3x + 2 = 0\} \) then \({(A \cap B)^ \subset }\) is
And
.
\(A = \{ x:{x^2} – 1 = 0,x \in z\} \) and \(B = \{ x:2{x^2} – 5x + 3 = 0,x \in z\} ,\) then \(A \cap B\) is equal to
.
If \(A = \{ x:{x^3} – 1 = 0,x \in z\} \) and \(B = \{ x:{x^2} – 2x + 1 = 0,x \in z\} ,\) then what is the relation between \(A\& B\)?
\[A = \{ x:{x^3} – 1 = 0,x \in z\} \]
All the above conditions are satisfied for relation between and .
Given \(n(A – B) = 3,n(B – A) = 4\) and \(n(A \cap B) = 2,\) then find \(n(A \cup B)\)?
If \(A\) and \(B\) are disjoint sets, \(n(A) = 3,n(B) = 5,\) then \(n(A \cap B)\) is equal to
Since, and are disjoint sets, they have no common elements. Hence, .
.
If \(n(A) = 3,n(B) = 5\) and \(n(A \cup B) = 8\) then \(n[P(A \cap B)]\) is equal to
Hence, and are disjoint
or
.
If \(A = \{ x:{x^2} – x – 2 = 9,x \in z\} \) and \(B = \{ x:{x^3} – 1 = 0,x \in z\} \), then
or
.
If \(A = \{ 1,2,3,4\} ,B = \{ 2,3,4\} ,\) and \(C = \{ \{ \} ,\{ 2\} ,\{ 3\} ,\{ 4\} ,\{ 2,3\} ,\{ 2,4\} ,\{ 3,4\} ,\{ 2,3,4\} \} \). What is the relation between \(A,B\) and \(C\)?
.
If \(A = \{ 1,2,3,4\} \) and \(B = \{ \{ 1\} ,\{ 2\} ,\{ 3\} ,\{ 4\} \} \), then \(A \cap B\) is equal to
No elements of contains in or no elements of contains in .
.
If \[A = \phi \] and \(B = \{ \phi \} \), Determine the relation between \(A\) and \(B\)?
is an element of .
.
\(A = \{ a,b\} ,B = \{ a,b,c\} ,C = \{ c,a,b\} \). Find the relation between \(A.B\) and \(C\)?
.
If \(A,B\) and \(C\) are disjoint sets, then \(n(A \cup B \cup C)\) is equal to
Since, and are disjoints
.
In a class of 75 students, if 30 eat sweets, 35 eats chocolates and 15 eat both the items, then the number of students who don’t eat these items is
Let be total number of students.
Let number of students eat sweets & numbers of students eat chocolate.
So, number of students who do not eat both items is
In a survey of 400 students in a school, 200 were taking apple juice, 175 were taking orange juice and 125 were taking both the juice. How many students were taking neither apple juice nor orange juice?
So, number of students were taking neither juice
In a survey 21 people like product \(A\), 26 like product \(B\) and 29 liked product \(C\), If 14 people like \(A\) and \(B\) , 12 like \(B\) and \(C\), 10 like \(C\) and \(A\) and 8 like all the three product. Find the total number of people?
.
In a group, 100 can speak ODIA, 80 can speak HINDI, 75 can speak ENGLISH, 40 can speak ODIA & HINDI, 50 can speak ODIA & ENGLISH, 45 can speak HINDI & ENGLISH. If the total number of people in this group is 150. Then, find how many people can speak three languages?
For any sets \(A\) and \(B\), \((A \cap B) – A\) is equal to
(DeMorgan’s law)
(Associative law)
\({(A \cup B)^ \subset } – {B^ \subset }\) is equal to _______, where \(A\) and \(B\) are any sets.
(DeMorgan’s law)
(Associative law)
Let \(A = \{ {x^y},{y^x}\} \), the \(P(A)\) is equal to
.
\(A = \{ x;x\) is an integer which is both even and odd\(\} \), \(B = \{ x:x\) is an integer and \(x \ne x\} \), then \(A \cup B\) is equal to
is an integer which is both even and odd
(Because any integer can’t be both even and odd)
is an integer and
.
If \(A\) and \(B\) are sets, and \(A = \{ 1,2,3,4\} ,B = \{ x:x\) is a divisor of \(60,x \in N\} \), \(A\) and \(B\)is related to
is a divisor of
.
If \(A = \phi \)A, then \(n[P(P(A))]\) is equal to
.
If \(A\) and \(B\) are any sets, \(n(A) = 3,n(B) = 4,n(A \cap B)2,\) then \(n[P(A \cup B)]\) is equal to
.
have 5 elements.
.