CSC $1500-$ HOMEWORK $2$: Equivalences and Validations

$(1)$ Turn the following phrases into logical statements.

$(1.$Ex$)$ Either you can go to the MOVIES, or you can obey QUARANTINE $($but

you can't do both!$)$

MOVIES XOR QUARANTINE

$(1\mathrm{.}1)$ If I get out to a RESTAURANT, then I$\text{'}$m expecting to have a nice MEAL

or good SERVICE. $(5$pts$.)$

$(1\mathrm{.}2)$ I will bake a cake or make pasta, but only if Steve comes home and

he's healthy. $(10$pts$.)$

$(2)$ State the logical equivalences needed in order to turn statement $1$ into

statement $2.$

$(2.$Ex$)$

Statement $1$: $(!$A or $(!$B and $!$C$))$ and $($B or $!$B$)$

Statement $2$: $($A nand $($B or C$))$

$(!$A or $(!$B and $!$C$))$ and $($B or $!$B$)-$NEGATION$-(!$A or $(!$B and $!$C$))$ and

TRUE

$(!$A or $(!$B and $!$C$))$ and TRUE $-$IDENTITY$-(!$A or $(!$B and $!$C$))$

$(!$A or $(!$B and $!$C$))-$DE MORGAN$-(!$A or $!($B or $C))$

$(!$A or $!($B or $C))-$DE MORGAN AGAIN$-!($A and $($B or $C))-$SAME$-($A

nand or $C)$

$(2\mathrm{.}1)(1$Opts.$)$

Statement $1$: $($D and $(!$D or E$))$

Statement $2$: $($D and E$)$

$(2\mathrm{.}2)(1$Opts.$)$