Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional.
-The lights are on if and only if it is not midnight or it is wintertime.
A) $\mathrm { p } \leftrightarrow ( \sim \mathrm { q } \vee \mathrm { r } )$; biconditional
B) $( \mathrm { p } \leftrightarrow \sim \mathrm { q } ) \wedge \mathrm { r }$; conjunction
C) $( \mathrm { p } \leftrightarrow \sim \mathrm { q } ) \vee \mathrm { r }$; disjunction
D) $\mathrm { p } \leftrightarrow ( \sim \mathrm { q } \vee \mathrm { r } )$; conditional

Question

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional.
-The lights are on if and only if it is not midnight or it is wintertime. 
A) $\mathrm { p } \leftrightarrow ( \sim \mathrm { q } \vee \mathrm { r } )$; biconditional
B) $( \mathrm { p } \leftrightarrow \sim \mathrm { q } ) \wedge \mathrm { r }$; conjunction
C) $( \mathrm { p } \leftrightarrow \sim \mathrm { q } ) \vee \mathrm { r }$; disjunction
D) $\mathrm { p } \leftrightarrow ( \sim \mathrm { q } \vee \mathrm { r } )$; conditional

Quizplus · Accepted Answer

The correct symbolic representation of the statement "The lights are on if and only if it is not midnight or it is wintertime" is a biconditional statement, which is correctly represented in option A as $\mathrm { p } \leftrightarrow ( \sim \mathrm { q } \vee \mathrm { r } )$. This means "p if and only if not q or r".

Select Letters to Represent the Simple Statements and Write Each p↔(∼q∨r)\mathrm { p } \leftrightarrow ( \sim \mathrm { q } \vee \mathrm { r } )p↔(∼q∨r)

Select Letters to Represent the Simple Statements and Write Each $\mathrm { p } \leftrightarrow ( \sim \mathrm { q } \vee \mathrm { r } )$