Answer
$E\cup I^{\prime}$
Work Step by Step
$E\cap F$ represents the event that both $E$ and $F$ occur.
$E\cup F$ represents the event that $E$ occurs or $F$ occurs (or both)$\\\\$
The complement of $E,\ E^{\prime}$ represents the event that $E$ does not occur.
W: you will use the book's Website tonight,$\\\\$
I: your math grade will improve, $\\\\$
E: you will use the Website every night$.\\\\$
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$($you will use the Website every night$) $ OR (your math grade will not improve)
(E occurs) OR (I does not occur)
$\rightarrow$ $\mathrm{E}\cup I^{\prime}$
