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.
-If a number is divisible by 3 and the number is not divisible by 2 then the number is not divisible By 6.
A) $\mathrm { p } \wedge ( \sim \mathrm { q } \rightarrow \sim \mathrm { r } )$; conjunction
B) $\mathrm { p } \vee ( \sim \mathrm { q } \rightarrow \sim \mathrm { r } )$; disjunction
C) $( \mathrm { p } \wedge \sim \mathrm { q } ) \leftrightarrow ( \sim \mathrm { r } )$; biconditional
D) $( \mathrm { p } \wedge \sim \mathrm { q } ) \rightarrow ( \sim \mathrm { r } )$; 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.
-If a number is divisible by 3 and the number is not divisible by 2 then the number is not divisible By 6. 
A) $\mathrm { p } \wedge ( \sim \mathrm { q } \rightarrow \sim \mathrm { r } )$; conjunction
B) $\mathrm { p } \vee ( \sim \mathrm { q } \rightarrow \sim \mathrm { r } )$; disjunction
C) $( \mathrm { p } \wedge \sim \mathrm { q } ) \leftrightarrow ( \sim \mathrm { r } )$; biconditional
D) $( \mathrm { p } \wedge \sim \mathrm { q } ) \rightarrow ( \sim \mathrm { r } )$; conditional

Quizplus · Accepted Answer

The statement is a conditional statement because it has the form "if...then...". It states that if a number is divisible by 3 and not divisible by 2, then it is not divisible by 6. This is represented by $( \mathrm { p } \wedge \sim \mathrm { q } ) \rightarrow ( \sim \mathrm { r } )$, where $p$ is "a number is divisible by 3", $\sim q$ is "the number is not divisible by 2", and $\sim r$ is "the number is not divisible by 6".

Select Letters to Represent the Simple Statements and Write Each p∧(∼q→∼r)\mathrm { p } \wedge ( \sim \mathrm { q } \rightarrow \sim \mathrm { r } )p∧(∼q→∼r)

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