Remove renundant tuples from $|(X \times Y) \cup (Y \times X)|$ to calculate cardinality

Question

let $X=\{9,5,6,0,4,2,1,4\}$

$Y=\{0,3,9,6,7,1\}$

Calculate $|(X \times Y) \cup (Y \times X)|$

My solution is $|X \times Y| + |Y \times X| - |\{9,6,0,1\} \times \{0,9,6,1\}|= 40 + 40 - 16 = 64$

However the correct result should be $68$. Question: Where is my mistake and how to get that result? I think I have removed the double tuples with $|\{9,6,0,1\} \times \{0,9,6,1\}|$

Answer 1

Your method is entirely correct, the only mistake you made was thinking that $|X\times Y| = 40$. Remember, the size of $X\times Y$ is always $|X|\cdot |Y|$, and in your case, that would be $7\cdot 6$, which is not equal to $40$...