Question:
In the group $\{1, 2, 3, 4, 5, 6\}$ under multiplication modulo $7$, if $5x = 4$, then $x =$
In the group $\{1, 2, 3, 4, 5, 6\}$ under multiplication modulo $7$, if $5x = 4$, then $x =$
Updated On: May 12, 2024
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The Correct Option is A
Solution and Explanation
$\{1, 2, 3, 4, 5, 6\}$ is a group under multiplication and 1 is the identity element
$\Rightarrow \, 5^{-1} =3$
Now, $5x=4$
$5^{-1} 5x = 5^{-1} 4 (mod 7) \Righatrrow x = 3.4$ (mod 7)
$\Rightarrow \, x=5 (mod \: 7)$
$\Rightarrow \, 5^{-1} =3$
Now, $5x=4$
$5^{-1} 5x = 5^{-1} 4 (mod 7) \Righatrrow x = 3.4$ (mod 7)
$\Rightarrow \, x=5 (mod \: 7)$
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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
