Monday, February 4, 2019

elementary set theory - Can these two sets be equipotent?

Equipotent: A is equipotent to B if A bijective to B



Bijective: A is bijective to B if A is injective and Surjective



X = 10 elements
A = {Y $\subseteq$ X | Y has 7 elements}
B = {Z $\subseteq$ X | Z has 3 elements}




Show that A $\approx$ B



Now, can this be equipotent?



if X={0,1,2,3,4,5,6,7,8,9}
Y={0,1,2,3,4,5,6}
Z={7,8,9}



As fas as I know this two sets have diferent number of elements, so it will be A being only surjective to B, but not injective



Thanks in advance for the answer.

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