Set theory practice · Easy

Let $S = \left\{ {\theta \in [0,2\pi ]:{8^{2{{\sin }^2}}}\theta + {8^{2{{\cos }^2}\theta }} = 16} \right\}.$ Then $n(S)+$ $\sum\limits_{\theta \in S} {\left( {\sec \left( {\frac{\pi }{4} + 2\theta } \right)\cos ec\left( {\frac{\pi }{4} + 2\theta } \right)} \right)}$ is equal to :

If the number of elements in $A$ is $m$ and number of element in $B$ is $n$ then the number of elements in the power set of $A \times B$ is

If $A=\{1,2,3\}, B=\{3,4,5\},$ then $(A \cap B) \times A$ is

Given the sets $A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\}$, then: $A \cup(B \cap C)$ is

If $X$ and $Y$ are two sets, then $X \cap(Y \cap X)^{\prime}$ equals

Let $\mathcal{U}$ be the universal set for sets A and B such that $n\left( A \right) = 200,n\left( B \right) = 300$ and $n\left( {A \cap B} \right) = 100.$ Then, $n\left( {A' \cap B'} \right)$ is equal to 300, provided that $n\left( \mathcal{U} \right)$ is equal to

Two finite sets have $m$ and $n$ elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of $m$ and $n$ are

If $A = \left\{ {1,\;2,\;3} \right\},\;B\left\{ {3,\;4} \right\},\;C\left\{ {4,\;5,\;6} \right\}$. Then, $A \cup \left( {B \cap C} \right)$ is

The value of $n\{P[P(\phi)]\}$ is equal to

For any two sets $A$ and $B$, $A - \left( {A - B} \right)$ equals

If $A$ and $B$ are two given sets, then $A \cap {\left( {A \cap B} \right)^c}$ is equal to

The set $(A \backslash B) \cup(B \backslash A)$ is equal to

If $A = \left\{ {x,\;y} \right\}$, then the power set of $A$ is

If $A,B$ and $C$ are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$, then

Statement-I: The set $\left\{x\right.$ : $x$ is a real number and $\left.x^2-1=0\right\}$ is the empty set.

Statement-II: The set ${A}=\left\{{x}: {x} \in {R}, {x}^2=16\right.$ and $\left.2 {x}=6\right\}$ is an empty set.

Let $f(x)=(x+1)^2-1,(x \geq-1)$. Then, the set $S=\left\{x: f(x)=f^{-1}(x)\right\}$ is

If $A$ and $B$ are two sets, then $(A-B) \cup(B-A) \cup(A \cap B)$ is equal to

The number of elements of the power set of a set containing $n$ elements is

If $A=\{1,2,5\}$ and $B=\{3,4,5,9\}$, then $A \Delta B$ is equal to

Which one of the following is $(A-B) \cup(B-A)$ ?

In a rehabilitation programme, a group of 50 families were assured new houses and compensation by the government. Number of families who got both is equal to the number of families who got neither of the two. The number of families who got new houses is 6 greater than the number of families who got compensation. How many families got houses?

If $A=\{2,3,4,8,10\}, B=\{3,4,5,10,12\}$ and $C=\{4, 5,6,12,14\}$, then $(A \cap B) \cup(A \cap C)$ is equal to

The finite sets $A$ and $B$ have m and n elements respectively. if the total number of subsets of $A$ is 112 more than the total number of subsets of $B$, then the volume of $m$ is

If $A=\{1,2,3\}$ and $B=\{3,8\}$, then $(A \cup B) \times(A \cap B)$ is

If a set $A=\{a, b, c\}$ then the number of subsets of the set $A$ is

Let $A$ and $B$ be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of the set $A$ is 56 more than the total number of subsets of $B.$ Then the distance of the point $P(m, n)$ from the point $Q(-2,-3)$ is:

If $A$ and $B$ are any two sets, then $A \cup(A \cap B)$ is equal to:

If ${U}=\{1,2,3\}$ and ${A}=\{1,2\}$ then $[{P}({A})]^{\prime}=$

Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If $K$% of them are suffering from both ailments, then $K$ cannot belong to the set

Let $A$ and $B$ have 3 and 6 elements respectively. What can be the minimum number of elements in $A \cup B?$