# Value of Sets - Union and Intersection [closed]

I would like to know the best way to answer this question!

Assume that $$| A ∩ B |= 13$$, $$| A |= 17$$ and $$| B |= 19$$. Determine the value of $$| A ∪ B |$$.

Regards!

## closed as off-topic by Gregory J. Puleo, Saad, John Omielan, N. F. Taussig, Alexander Gruber♦Apr 28 at 8:18

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• Start by drawing a Venn diagram. – Randall Apr 26 at 2:32

This is best done through the inclusion-exclusion principle. Venn diagrams are helpful as a visual. Formulaically, though, inclusion-exclusion gives us

$$|A \cup B| = |A| + |B| - |A \cap B|$$

Substitute in the appropriate values and you should be good to go.

• Thank you so, 17+19 = 36 - 13 = 23? So the answer must be 23! – AGRHQ Apr 26 at 2:36
• Well, to nitpick, you should write it as $17+19=36$ followed by $36-13=23$ (the way you wrote it suggests $17+19=23$, though I get what you meant by it). But yes, $23$ is correct. – Eevee Trainer Apr 26 at 2:37
• Thank youuuuuuu – AGRHQ Apr 26 at 2:38

$$A$$ contains $$17$$ things. $$B$$ contains $$19$$ things. Some of those things are in both sets. $$13$$, in fact. So, $$13$$ of the things are counted twice if we add $$|A|+|B|$$. How can we correct the overestimate of $$17+19=36$$? Does this get you started?

• Thank you I now understand 17+19=36, 36-13=23! – AGRHQ Apr 26 at 2:37
• Eevee's answer is the formula, and mine is how it works. Both good to know. And you are welcome. – The Count Apr 26 at 2:38