Question

11. Suppose that a, b, c, x are elements of a group G such that axcba^{-1} = b. Which one of the following is a correct expression for x? (a) x = a^{-1}ba(cb)^{-1} (b) x = (ba)^{-1}c^{-1}ba (c) x = a^{-1}b(cb)^{-1}a (d) x = c^{-1}(ba^{-1})^{-1}a^{-1}b (e) x = (ba^{-1})^{-1}a^{-1}bc^{-1}

          11. Suppose that a, b, c, x are elements of a group G such that
axcba^{-1} = b.
Which one of the following is a correct expression for x?
(a) x = a^{-1}ba(cb)^{-1}
(b) x = (ba)^{-1}c^{-1}ba
(c) x = a^{-1}b(cb)^{-1}a
(d) x = c^{-1}(ba^{-1})^{-1}a^{-1}b
(e) x = (ba^{-1})^{-1}a^{-1}bc^{-1}

11. Suppose that a, b, c, x are elements of a group G such that
axcba^-1 = b.
Which one of the following is a correct expression for x?
(a) x = a^-1ba(cb)^-1
(b) x = (ba)^-1c^-1ba
(c) x = a^-1b(cb)^-1a
(d) x = c^-1(ba^-1)^-1a^-1b
(e) x = (ba^-1)^-1a^-1bc^-1

Added by Enrique S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/01/2023

Step 1

We want to find an expression for $w = a^{-1}ba(cb)^{-1}$. First, let's find $(cb)^{-1}$. Since $(ab)^{-1} = b^{-1}a^{-1}$, we have $(cb)^{-1} = b^{-1}c^{-1}$. Now, let's substitute this into the expression for $w$: $w = a^{-1}ba(cb)^{-1} = Show more…

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Suppose that a, b, c, x are elements of a group G such that axcba^-1 = b. Which one of the following is a correct expression for x? (a) x = a^-1ba(cb)^-1 (d) x = c^-1(ba^-1)^-1a^-1b (b) x = (ba)^-1c^-1ba (c) x = a^-1b(cb)^-1a