Find $\left| A _ { 1 } \cup A _ { 2 } \cup A _ { 3 } \cup A _ { 4 } \right|$

question 113

Short Answer

Find $\left| A _ { 1 } \cup A _ { 2 } \cup A _ { 3 } \cup A _ { 4 } \right|$ if each set A_i has 150 elements, each intersection of two sets has 80 elements, each intersection of three sets has 20 elements, and there are no elements in all four sets.

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Definitions:

Inverse Function

A function that reverses the operations of a given function, such that applying both functions in succession results in the original value.

Square Root

The value that, when multiplied by itself, yields the original number; it is denoted as \(\sqrt{x}\) for a number \(x\).

Logarithm

The power to which a base, often 10 or e, must be raised to produce a given number.

Logarithm

The exponent or power to which a base must be raised to yield a given number.