Question:
Write down all the subsets of the following sets:
(i) {a}
(ii) {a, b}
(iii) {1, 2, 3}
(iv) \(\phi\)
Write down all the subsets of the following sets:
(i) {a}
(ii) {a, b}
(iii) {1, 2, 3}
(iv) \(\phi\)
(i) {a}
(ii) {a, b}
(iii) {1, 2, 3}
(iv) \(\phi\)
Updated On: Oct 22, 2023
Hide Solution
Verified By Collegedunia
Solution and Explanation
(i) The subsets of {a} are \(\phi\) and {a}.
(ii) The subsets of {a, b} are \(\phi\), {a}, {b}, and {a, b}.
(iii) The subsets of {1, 2, 3} are \(\phi\), {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, and {1, 2, 3}
(iv) The only subset of \(\phi\) is \(\phi\).
Was this answer helpful?
0
0
Top Questions on Subsets
- The sum of the first \(n\) natural numbers is:
- Let \( E \subset F \) and \( F \subset K \) be field extensions which are not algebraic. Let \( \alpha \in K \) be algebraic over \( F \) and \( \alpha \notin F \). Let \( L \) be the subfield of \( K \) generated over \( E \) by the coefficients of the monic polynomial of minimal degree over \( F \) which has \( \alpha \) as a zero. Then, which of the following is/are TRUE?
- All rings considered below are assumed to be associative and commutative with \( 1 \neq 0 \). Further, all ring homomorphisms map 1 to 1.
Consider the following statements about such a ring \( R \):
P1: \( R \) is isomorphic to the product of two rings \( R_1 \) and \( R_2 \).
P2: \( \exists r_1, r_2 \in R \) such that \( r_1^2 = r_1 \neq 0 \), \( r_2^2 = 0 \), and \( r_1 + r_2 = 1 \).
P3: \( R \) has ideals \( I_1, I_2 \subset R \) with \( R \neq I_1 \), \( (0) \neq I_2 \), and \( R = I_1 + I_2 \) and \( I_1 \cap I_2 = (0) \).
P4: \( \exists a, b \in R \) with \( a \neq 0 \), \( b \neq 0 \) such that \( ab = 0 \).
Then, which of the following is/are TRUE? - Let \( X \) be an uncountable set. Let the topology on \( X \) be defined by declaring a subset \( U \subset X \) to be open if \( X - U \) is either empty or finite or countable, and the empty set to be open. Then, which of the following is/are TRUE?
- In the following, all subsets of Euclidean spaces are considered with the respective subspace topologies. Define an equivalence relation \( \sim \) on the sphere \[ S = \left\{ (x_1, x_2, x_3) \in \mathbb{R}^3 : x_1^2 + x_2^2 + x_3^2 = 1 \right\} \] by \( (x_1, x_2, x_3) \sim (y_1, y_2, y_3) \) if \( x_3 = y_3 \), for \( (x_1, x_2, x_3), (y_1, y_2, y_3) \in S \). Let \( [x_1, x_2, x_3] \) denote the equivalence class of \( (x_1, x_2, x_3) \), and let \( X \) denote the set of all such equivalence classes. Let \( L : S \to X \) be given by \[ L\left( (x_1, x_2, x_3) \right) = [x_1, x_2, x_3]. \] If \( X \) is provided with the quotient topology induced by the map \( L \), then which one of the following is TRUE?
View More Questions
Questions Asked in CBSE Class XI exam
(i) List the deeds that led Ray Johnson to describe Akhenaten as “wacky”.
(ii) What were the results of the CT scan?
(iii) List the advances in technology that have improved forensic analysis.
(iv) Explain the statement, “King Tut is one of the first mummies to be scanned — in death, as in life...”- CBSE Class XI
- Discovering Tut: The saga Continues
Give reasons for the following.
(i) King Tut’s body has been subjected to repeated scrutiny.
(ii) Howard Carter’s investigation was resented.
(iii) Carter had to chisel away the solidified resins to raise the king’s remains.
(iv) Tut’s body was buried along with gilded treasures.
(v) The boy king changed his name from Tutankhaten to Tutankhamun.- CBSE Class XI
- Discovering Tut: The saga Continues
- Write a note on economic importance of algae and gymnosperms.
- CBSE Class XI
- Bryophytes
- Briefly comment on "The author’s meeting with Norbu."
- CBSE Class XI
- Silk road
- The story revolves around characters who belong to a tribe in Armenia. Mourad and Aram are members of the Garoghlanian family. Now locate Armenia and Assyria on the atlas and prepare a write-up on the Garoghlanian tribes. You may write about people, their names, traits, geographical and economic features as suggested in the story.
- CBSE Class XI
- The summer of the beautiful white horse
View More Questions
Concepts Used:
Types of Sets
Sets are of various types depending on their features. They are as follows:
- Empty Set - It is a set that has no element in it. It is also called a null or void set and is denoted by Φ or {}.
- Singleton Set - It is a set that contains only one element.
- Finite Set - A set that has a finite number of elements in it.
- Infinite Set - A set that has an infinite number of elements in it.
- Equal Set - Sets in which elements of one set are similar to elements of another set. The sequence of elements can be any but the same elements exist in both sets.
- Sub Set - Set X will be a subset of Y if all the elements of set X are the same as the element of set Y.
- Power Set - It is the collection of all subsets of a set X.
- Universal Set - A basic set that has all the elements of other sets and forms the base for all other sets.
- Disjoint Set - If there is no common element between two sets, i.e if there is no element of Set A present in Set B and vice versa, then they are called disjoint sets.
- Overlapping Set - It is the set of two sets that have at least one common element, called overlapping sets.