IMathAS-libretexts

Rewrite the following statement in symbolic logic.

"Winning the lottery is neccessary and sufficient for becoming a multimillionaire overnight, but I won't tell you if I win."

A: I win the lottery.

B: I become a multimillionaire overnight.

C: I will tell you.

D: I win.

$\displaystyle {\left({A}\leftrightarrow{B}\right)}\wedge{\left({C}\rightarrow{D}\right)}$
$\displaystyle {\left({A}\leftarrow{B}\right)}\vee{\left({D}\rightarrow{C}\right)}$
$\displaystyle {\left({A}\rightarrow{B}\right)}\wedge{(}$ ~ $\displaystyle {C}\rightarrow{D}{)}$
$\displaystyle {\left({A}\leftrightarrow{B}\right)}\vee{(}$ ~ $\displaystyle {C}\rightarrow{D}{)}$
$\displaystyle {\left({B}\leftrightarrow{A}\right)}\wedge{\left({D}\rightarrow\right.}$ ~ $\displaystyle {C}{)}$

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