Logical equivalence

It is a relationship between two propositions where their truth tables are identical.

• biconditional

• conditional

• logical equivalence

• negation

It is a proposition in the form 

 $"If\ p\ then\ q".$  

• conjunction

• conditional

• disjunction

• negation

It is a proposition in the form

 $"p\ if\ and\ only\ if\ q".$  

• biconditional

• conditional

• logical equivalence

• negation

The proposition “If it is not rainy, then it is sunny” is a __________ statement.

• conjunction

• conditional

• disjunction

• negation

The proposition “Lhea will go to church if and only if it is sunny day” is a ___________________.

• biconditional statement

• conditional statement

• disjunction statement

• negation

Which of the following are logically equivalent?

• $p\vee q\ and\ q\wedge p$

• $\left(p\wedge q\right)\rightarrow p\ and\ \left(p\wedge q\right)\rightarrow q$

• $\left(p\wedge q\right)\rightarrow p\ and\ q\rightarrow\left(p\wedge q\right)$

• $p\rightarrow\left(p\wedge q\right)\ and\ \left(p\wedge q\right)\rightarrow q$

Let
 $p:$ The soup is tasty.
 $q:$  The soup is too hot.

Express the proposition “The soup is tasty if and only if it is not too hot” in symbols.

•  $p\rightarrow\sim q$  

•  $p\leftrightarrow\sim q$  

•  $p\vee\sim q$  

•  $p\wedge\sim q$  

Which of the following is the correct truth table of  $p↔∼q$ ?

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If Lhea will go to school, then she will read and write.
Using the variables  $p,q,\ and\ r$ , which of the following is the correct truth table of the given proposition?

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Sophia will go to church if and only if today is a sunny or windy day.
Using the variables $p,q\ and\ r$ , which of the following is the correct truth table of the given proposition?

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