Question

suppose set a contains 97 elements and set b contains 67 elements. if the total number elements in either set a or set b is 132, how many elements do sets a and b have in common?

Answer 1

Answer:

• 32 elements

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Use the formula for the union of two sets:

• |A ∪ B| = |A| + |B| - |A ∩ B|

In this case, we have:

• |A ∪ B| = 132,
• |A| = 97, and
• |B| = 67.

Plugging these values into the formula:

• 132 = 97 + 67 - |A ∩ B|

Now, solve for |A ∩ B| (the number of elements in common):

• |A ∩ B| = 97 + 67 - 132
• |A ∩ B| = 164 - 132
• |A ∩ B| = 32

So, sets A and B have 32 elements in common.