Week 9 - Algebraic distance, permutations

About permutations, choose the CORRECT information.

a) Let α = (a b c) and β be a 2-cycle permutation containing a, b and c. The total number of cycles in αβ will be less than the number of cycles in β.
b) Let α = (a b) and β be any permutation. If a and b are in the same cycle on the cycle decomposition of β, then this cycle will be partitioned into two on the cycle decomposition of αβ.
c) Let α = (a b) and β be any permutation. If a and b are in separate cycles on the cycle decomposition of β, they will turn into a unique cycle on the decomposition of αβ.
d) Given a permutation α, its inverse α^-1 is obtained by the inverse of the cycle decomposition of each cycle in α.
e) None of the above.

Translated by: Raphael Cristofaro
Original idea by: Kaio Karam