I don't understand it.(adsbygoogle = window.adsbygoogle || []).push({});

A has n elements, and B has m elements. Give the exact maximum/minimum of

1) A [itex]\bigcup[/itex] B

2) A [itex]\bigcap[/itex] B

3) A X B

I don't understand the solution to this..

1) If A and B are a disjunction ( A[itex]\bigcap[/itex] B = ∅), then the max of A [itex]\bigcup[/itex] B is:

A [itex]\bigcap[/itex] B = ∅ -> |A[itex]\bigcup[/itex]B| = m + n

If A is a subset of B (A[itex]\subseteq[/itex]B) or B a subset of A (B [itex]\subseteq[/itex] A),

then the min of A and B is:

A[itex]\subseteq[/itex]B -> |A[itex]\bigcup[/itex]B| = |B| = m

B[itex]\subseteq[/itex]A -> |A[itex]\bigcup[/itex]B| = |A| = n

So you're basically saying the min here is m and n. I understand that. I just don't get the explanation of it. I have to show why it's the min.

Therefore, the max of A [itex]\bigcup[/itex] B is:

max(n,m) [itex]\leq[/itex] |A[itex]\bigcup[/itex]B| [itex]\leq[/itex] n+m

Don't get this one. In words: The max is no greater than n+m. But it says it's less or equal to A and B. So you're already assuming A and B is the max?

2 and 3 have the same confusing explanations.

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# Logic - Unions

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