Question:
Which of the following is a subgroup of the group $G = \{1, 2, 3, 4, 5, 6\}$ under $\otimes_7$ ?
Which of the following is a subgroup of the group $G = \{1, 2, 3, 4, 5, 6\}$ under $\otimes_7$ ?
Updated On: May 11, 2024
- $\{2, 6, 1\}$
- $\{1, 2, 4\}$
- $\{5, 4, 2\}$
- $\{2, 3 , 1\}$
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
$G = \{1, 2, 3, 4, 5, 6\}, \oplus_7$
(a) $\{2, 6, 1) $ is not a subgroup
$\because 2\oplus_7 6=5 \notin \{ 2,6, 1 \}$
(b) $\{1, 2, 4\}$ is a subgroup
$\because$ it satisfies all properties of group.
$ 1\oplus_7 2=2, 2 \oplus_7 4=1,4 \oplus_7 1=4$
(c) $ \{5, 4, 2 \}$ is not a subgroup ?
$\because $ In this set identity element do not exist.
(d) $ \{2, 3, 1\} $ is not a subgroup
$\because 2 \oplus_7 3 = 6 \notin \{2, 3, 1\}$
(a) $\{2, 6, 1) $ is not a subgroup
$\because 2\oplus_7 6=5 \notin \{ 2,6, 1 \}$
(b) $\{1, 2, 4\}$ is a subgroup
$\because$ it satisfies all properties of group.
$ 1\oplus_7 2=2, 2 \oplus_7 4=1,4 \oplus_7 1=4$
(c) $ \{5, 4, 2 \}$ is not a subgroup ?
$\because $ In this set identity element do not exist.
(d) $ \{2, 3, 1\} $ is not a subgroup
$\because 2 \oplus_7 3 = 6 \notin \{2, 3, 1\}$
Was this answer helpful?
0
0
Top Questions on Relations and functions
- If the domain of the function \( f(x) = \log_e \left( \frac{2x + 3}{4x^2 + x - 3} \right) + \cos^{-1} \left( \frac{2x - 1}{x + 2} \right) \) is \( (\alpha, \beta] \), then the value of \( 5\beta - 4\alpha \) is equal to
- JEE Main - 2024
- Mathematics
- Relations and functions
- Consider the relations $R_1$ and $R_2$ defined as \[a R_1 b \iff a^2 + b^2 = 1 \quad \text{for all } a, b \in \mathbb{R},\]and \[(a, b) R_2 (c, d) \iff a + d = b + c \quad \text{for all } (a, b), (c, d) \in \mathbb{N} \times \mathbb{N}.\]Then:
- JEE Main - 2024
- Mathematics
- Relations and functions
- Let the relations \( R_1 \) and \( R_2 \) on the set
\( X = \{ 1, 2, 3, \dots, 20 \} \) be given by
\( R_1 = \{ (x, y) : 2x - 3y = 2 \} \) and
\( R_2 = \{ (x, y) : -5x + 4y = 0 \} \).
If \( M \) and \( N \) be the minimum number of elements required to be added in \( R_1 \) and \( R_2 \), respectively, in order to make the relations symmetric, then \( M + N \) equals:- JEE Main - 2024
- Mathematics
- Relations and functions
- The interval in which the function \( f(x) = x^x, \, x>0 \), is strictly increasing is:
- JEE Main - 2024
- Mathematics
- Relations and functions
- The function \( f(x) = \frac{x^2 + 2x - 15}{x^2 - 4x + 9} \), \( x \in \mathbb{R} \) is:
- JEE Main - 2024
- Mathematics
- Relations and functions
View More Questions
Questions Asked in COMEDK UGET exam
- A $2\,kg$ mass lying on a table is displaced in the horizontal direction through $50\,cm$. The work done by the normal reaction will be
- COMEDK UGET - 2015
- work, energy and power
- The numbers of $ {H^+}$ ions present in 1 mL of a solution whose pH is 13
- COMEDK UGET - 2015
- Equilibrium
- A mixture of methylamine and dimethylamine is given to you. The reagents used to separate the components of the mixture are
- $\cot^{-1} (21) + \cot^{-1} (13) + \cot^{-1} (-8) =$
- COMEDK UGET - 2015
- Inverse Trigonometric Functions
- Pick the incorrect statement among those given below.
- COMEDK UGET - 2015
- Chemical bonding and molecular structure
View More Questions
Concepts Used:
Relations and functions
A relation R from a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, no two distinct elements of B have the same pre-image.
Representation of Relation and Function
Relations and functions can be represented in different forms such as arrow representation, algebraic form, set-builder form, graphically, roster form, and tabular form. Define a function f: A = {1, 2, 3} → B = {1, 4, 9} such that f(1) = 1, f(2) = 4, f(3) = 9. Now, represent this function in different forms.
- Set-builder form - {(x, y): f(x) = y2, x ∈ A, y ∈ B}
- Roster form - {(1, 1), (2, 4), (3, 9)}
- Arrow Representation
