Question:
If A= {a, b, c, d} then number of subsets of A are
If A= {a, b, c, d} then number of subsets of A are
Updated On: Apr 17, 2025
- 8
- 12
- 16
- 20
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
To solve the problem, we need to find the number of subsets of the set \( A = \{a, b, c, d\} \).
1. Understanding the Formula for Subsets:
If a set has \( n \) elements, then the total number of subsets is given by:
\( \text{Number of subsets} = 2^n \)
2. Count the Elements in the Set:
The set \( A = \{a, b, c, d\} \) has 4 elements. So, \( n = 4 \).
3. Apply the Formula:
Substitute \( n = 4 \) into the formula:
\( \text{Number of subsets} = 2^4 = 16 \)
Final Answer:
The number of subsets of set \( A \) is \( 16 \).
Was this answer helpful?
1
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 TS POLYCET exam
- The volume of CO\(_2\) liberated in litres at STP when 25 g of CaCO\(_3\) is treated with dilute HCl containing 14.6 g of HCl is:
- TS POLYCET - 2025
- Chemical Reactions
- Median of \( x, 20x, \frac{x}{20}, 200x, \frac{x}{200} \) (where \( x>0 \)) is 20, then the value of \( x \) is:
- TS POLYCET - 2025
- Solution of a Linear Equation
- The solution of system of equations \( \frac{x}{2025} + \frac{y}{2026} = 2 \) and \( \frac{2x}{2025} - \frac{y}{2026} = 1 \) is:
- TS POLYCET - 2025
- Lines and Angles
- The roots of the quadratic equation \( x^2 - 16 = 0 \) are:
- TS POLYCET - 2025
- Conic sections
- In the given figure, if \( \angle AOB = 125^\circ \), then \( \angle COD = \):
- TS POLYCET - 2025
- Collinearity of points
View More Questions