Discrete Mathematics

a) Write the proposition for the following English sentence:

1) a) If Benjamin have cough, fever, and no smell, Benjamin is COVID19 positive.

b) Write inverse, converse and countrapositive of English sentence in (A)

2) Let p and q be the propositions "The election is decided" and "The votes have been counted," respectively. Express each of these compound propositions as English sentences.

b) Proof using laws of logic

1) \(\displaystyle{\left({p}\wedge{q}\right)}\rightarrow{p}\) is tautology

2) \(\urcorner p\leftrightarrow q\Leftrightarrow p\leftrightarrow\urcorner q\)