In the group G = 1, 5, 7, 11 under otimes12 the value of 7 otimes12 11-1 is equal to

Question

In the group G = 1, 5, 7, 11 under otimes12 the value of 7 otimes12 11-1 is equal to (A) 5 (B) 7 (C) 11 (D) 1

Tardigrade Admin · Accepted Answer

G = 1, 5, 7,11 ⊕12 we know that 1 is an identity element. inverse of 11 is, 11 ⊕12 11-1 = 1 and 11 ⊕12 11 = 1 Hence 11-1 = 11. ∴ 7 ⊕12 11-1 = 7 ⊕12 11 = 5

Q. In the group $G = {1, 5, 7, 11}$ under $\otimes_{12}$ the value of $7 \otimes_{12} 1 1^{- 1}$ is equal to

5

7

11

1

$G = {1, 5, 7, 11}, \oplus_{12}$
we know that 1 is an identity element.
inverse of 11 is,
$11 \oplus_{12} 1 1^{- 1} = 1$ and $11 \oplus_{12} 11 = 1$
Hence $1 1^{- 1} = 11. ∴ 7 \oplus_{12} 1 1^{- 1} = 7 \oplus_{12} 11 = 5$

Q. In the group G={1,5,7,11} under ⊗12​ the value of 7⊗12​11−1 is equal to

5

7

11

1

G={1,5,7,11},⊕12​ we know that 1 is an identity element. inverse of 11 is, 11⊕12​11−1=1 and 11⊕12​11=1 Hence 11−1=11.∴7⊕12​11−1=7⊕12​11=5

Q. In the group $G = {1, 5, 7, 11}$ under $\otimes_{12}$ the value of $7 \otimes_{12} 1 1^{- 1}$ is equal to

$G = {1, 5, 7, 11}, \oplus_{12}$
we know that 1 is an identity element.
inverse of 11 is,
$11 \oplus_{12} 1 1^{- 1} = 1$ and $11 \oplus_{12} 11 = 1$
Hence $1 1^{- 1} = 11. ∴ 7 \oplus_{12} 1 1^{- 1} = 7 \oplus_{12} 11 = 5$