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If-P-a-b-c-d-c-d-a-b-Q-a-b-c-d-b-a-d-c-are-permutations-of-the-elements-a-b-c-d-then-QP-




Question Number 80340 by Rio Michael last updated on 02/Feb/20
If P =  ((a,b,c,d),(c,d,a,b) )  , Q =  ((a,b,c,d),(b,a,d,c) ) are  permutations of the elements (a,b,c,d), then   QP ≡
$$\mathrm{If}\:{P}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{c}}&{{d}}&{{a}}&{{b}}\end{pmatrix}\:\:,\:{Q}\:=\:\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{b}}&{{a}}&{{d}}&{{c}}\end{pmatrix}\:\mathrm{are} \\ $$$$\mathrm{permutations}\:\mathrm{of}\:\mathrm{the}\:\mathrm{elements}\:\left({a},{b},{c},{d}\right),\:\mathrm{then}\: \\ $$$${QP}\:\equiv \\ $$$$\: \\ $$
Answered by MJS last updated on 02/Feb/20
if QP means first Q then P  a→b→d  b→a→c  c→d→b  d→c→a  QP= ((a,b,c,d),(d,c,b,a) )
$$\mathrm{if}\:{QP}\:\mathrm{means}\:\mathrm{first}\:{Q}\:\mathrm{then}\:{P} \\ $$$${a}\rightarrow{b}\rightarrow{d} \\ $$$${b}\rightarrow{a}\rightarrow{c} \\ $$$${c}\rightarrow{d}\rightarrow{b} \\ $$$${d}\rightarrow{c}\rightarrow{a} \\ $$$${QP}=\begin{pmatrix}{{a}}&{{b}}&{{c}}&{{d}}\\{{d}}&{{c}}&{{b}}&{{a}}\end{pmatrix} \\ $$

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