Advertisements
Advertisements
Question
If A = |1, 2, 3, 4, 5|, then the number of proper subsets of A is
Options
(a) 120
(b) 30
(c) 31
(d) 32
Advertisements
Solution
(c) 31
The number of proper subsets of any set is given by the formula \[2^n - 1\] where n is the number of elements in the set.
Here,
n = 5
∴ Number of proper subsets of A =\[2^5 - 1 = 31\]
APPEARS IN
RELATED QUESTIONS
Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:
{2, 3, 4} _____ {1, 2, 3, 4, 5}
{a, b} ⊄ {b, c, a}
{a} ⊂ {a. b, c}
{a} ∈ (a, b, c)
Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?
{3, 4} ⊂ A
How many elements has P(A), if A = Φ?
Write the given intervals in set-builder form:
(–3, 0)
Write the following interval in set-builder form:
[–23, 5)
Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If x ∈ A and A ∈ B, then x ∈ B
Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If A ⊂ B and B ∈ C, then A ∈ C
Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If x ∈ A and A ⊄ B, then x ∈ B
If a set contains n elements, then write the number of elements in its power set.
If A and B are two sets such that \[n \left( A \right) = 20, n \left( B \right) = 25\]\text{ and } \[n \left( A \cup B \right) = 40\], then write \[n \left( A \cap B \right)\]
The number of subsets of a set containing n elements is
If A = {1, 3, 5, B} and B = {2, 4}, then
Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:
{x : x is a student of Class XI of your school} ____ {x : x student of your school}
Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:
{x : x is a triangle in a plane} _____ {x : x is a rectangle in the plane}
Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:
{x : x is an equilateral triangle in a plane} _____ {x : x is a triangle in the same plane}
Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:
{x : x is an even natural number} _____ {x : x is an integer}
Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?
{1, 2, 5} ⊂ A
Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?
{1, 2, 3} ⊂ A
Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?
Φ ∈ A
Write down all the subsets of the following set:
{a, b}
Write down all the subsets of the following set:
{1, 2, 3}
Write the following interval in Set-Builder form:
(– 3, 0)
If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by `n/2`
If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.
a ∈ Y but a2 ∉ Y
If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.
a is less than 6 and a ∈ Y
State True or False for the following statement.
If A is any set, then A ⊂ A.
State True or False for the following statement.
Given that M = {1, 2, 3, 4, 5, 6, 7, 8, 9} and if B = {1, 2, 3, 4, 5, 6, 7, 8, 9}, then B ⊄ M.
State True or False for the following statement.
The sets {1, 2, 3, 4} and {3, 4, 5, 6} are equal.
