Discrete math help Suppose A and B are sets with A B N Sho

Discrete math help:

Suppose A and B are sets with |A| = |B| = |N|. Show that |A B| = |N|

Solution

I assume u in \"A B\" is OR operation not the Union symbol as |A B| = |N| will fail for the union symbol

Given that |A| = |B| = |N|

that means number of elements in A = number of elements in B= number of elements in N

say number of elements in both =x then |A| = |B| = |N| =x ...(i)

then A v B will again give same number of elements in results

Hence |A v B |=x...(ii)

using (i) and (ii) we get :

|A v B| = |N|

Hence proved:)