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

question 154

Multiple Choice

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

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Definitions:

Long Term

Referring to an extended period, often implying a duration that affects future conditions or outcomes.

Structural Unemployment

A form of unemployment that arises from a mismatch between the skills that workers offer and the skills demanded by employers, often due to technological changes or market shifts.

Frictional Unemployment

Unemployment that occurs when people are between jobs or are entering the labor force for the first time.

Cyclical Unemployment

A type of unemployment that relates to the cyclical trends in the business cycle, increasing during recessions and decreasing in expansions.