Question

suppose set a contains 39 elements and the total number elements in either set a or set b is 80. if the sets a and b have 1 elements in common, how many elements are contained in set b?

Answer 1

• 42 elements

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Using the formula for the union of two sets:

• |A ∪ B| = |A| + |B| - |A ∩ B|

where

• |A| represents the number of elements in set A,
• |B| represents the number of elements in set B, and
• |A ∩ B| represents the number of elements in both sets A and B.

We are given that:

• |A| = 39
• |A ∩ B| = 1
• |A ∪ B| = 80

Plugging in the values, we get:

• 80 = 39 + |B| - 1
• |B| = 80 - 38
• |B| = 42

Therefore, set B contains 42 elements.