The cardinality of the set P(P(P($\phi$))) is
[P(A) represents power set of the set A]
- 0
- 1
- 2
- 4
The Correct Option is D
Solution and Explanation
Top Questions on cartesian products of sets
- Let $S =\{1,2,3,5,7,10,11\}$ The number of non-empty subsets of $S$ that have the sum of all elements a multiple of 3 , is _____
- JEE Main - 2023
- Mathematics
- cartesian products of sets
Let \(S ={ (\begin{matrix} -1 & 0 \\ a & b \end{matrix}), a,b, ∈(1,2,3,.....100)}\) and
let \(T_n = {A ∈ S : A^{n(n + 1)} = I}. \)
Then the number of elements in \(\bigcap_{n=1}^{100}\) \(T_n \) is- JEE Main - 2022
- Mathematics
- cartesian products of sets
- If the function $f: R \rightarrow R$ is defined by $f(x)=|x|(x-\sin x)$, then which of the following statements is TRUE?
- JEE Advanced - 2020
- Mathematics
- cartesian products of sets
- What is the least value of k such that the function x$^2$ + kx + 1 is strictly increasing on (1,2)
- VITEEE - 2006
- Mathematics
- cartesian products of sets
- Let $A=\{1,2,3,5,8,9\}$ Then the number of possible functions $f: A \rightarrow A$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to______
- Mathematics
- cartesian products of sets
Concepts Used:
Cartesian Products of Sets
Cartesian products of sets here are explained with the help of an example. Consider A and B to be the 2 sets such that A is a set of 3 colors of tables and B is a set of 3 colors of chairs objects, i.e.,
A = {red, blue, purple}
B = {brown, green, yellow},
Now let us find the number of pairs of colored objects that we can make from a set of tables and chairs in various combinations. They can be grouped as given below:
(red, brown), (red, green), (red, yellow), (blue, brown), (blue, green), (blue, yellow), (purple, brown), (purple, green), (purple, yellow)
There are 9 such pairs in the Cartesian product since 3 elements are there in each of the defined sets A and B. The above-ordered pairs shows the definition for the Cartesian product of sets given. This product is resembled by “A × B”.