I started to learn discrete mathematics using "Discrete mathematics and its Application" book. In this book exercises I couldn't find answer to the below question.
Let
$p$: I bought a lottery ticket this week.
$q$: I won the million dollar jackpot on Friday.
Translate $$\neg p \lor (p \land q)$$ to English.
On
Direct translation:
Either I did not buy a lottery ticket this week, or I bought a lottery ticket this week and I won the million dollar jackpot on Friday.
You can simplify this by relying on the logical equivalence of $\color\red{\neg{x}\vee{y}}$ and $\color\green{{x}\implies{y}}$.
Thus $\color\red{\neg{p}\vee({p}\wedge{q})}$ is equivalent to $\color\green{{p}\implies{p}\wedge{q}}$, which is quivalent to ${p}\implies{q}$.
Hence your statement can be translated to:
If I bought a lottery ticket this week, then I won the million dollar jackpot on Friday.
Let us do it in steps.
First, we just replace the symbols by their 'word' analogues.
Second, let us smooth the sentence.
Third, let us think about what the sentence means.
There are two options 'I did not buy' or 'I did buy'; in the second case 'I won.' This means if I did buy, then I did win. So:
Generally $\neg p \lor (p \land q)$ expresses "If p, then q."