Question Number 117972 by Ar Brandon last updated on 14/Oct/20
$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{surjections}\:\mathrm{of}\:\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\right\}\:\mathrm{onto}\:\left\{\mathrm{x},\mathrm{y}\right\}\:\mathrm{is} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{16}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{14}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{6} \\ $$
Answered by Lordose last updated on 14/Oct/20
$$\mathrm{N}=\:\mathrm{2}^{\mathrm{n}\left(\mathrm{A}\right)−\mathrm{1}} =\:\mathrm{2}^{\mathrm{3}} =\mathrm{8} \\ $$$$\mathrm{Guessed} \\ $$
Commented by Ar Brandon last updated on 14/Oct/20
Thanks
Commented by Ar Brandon last updated on 14/Oct/20
Is it a formula ?
Commented by Lordose last updated on 14/Oct/20
It's like (2ⁿ ÷ 2) since it {x,y}
Commented by Ar Brandon last updated on 14/Oct/20
OK thanks ��
Commented by Ar Brandon last updated on 14/Oct/20
Oops ! Sorry to trouble you. C.14 is the correct answer from my book. But there isn't any demonstration.
Answered by bemath last updated on 14/Oct/20
$$\mathrm{2}^{\mathrm{4}} \:=\:\mathrm{16} \\ $$