Biconditionals

Lessons

• Introduction
  Biconditionals Overview:
  a)

  What are Biconditionals
  
  

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• 1.
  Forming the Biconditional
  Write a biconditional using the given conditionals:
  a)

  If today is Monday, then yesterday was Sunday.
  If yesterday was Sunday, then today is Monday
  
  
  b)

  If he drives faster than 100 km, then he will get a ticket.
  If he gets a ticket, then he has driven faster than 100 km.
  
  
  c)

  If today is the weekend, then I do not go to school.
  If I do not go to school, then it is the weekend.
  
  

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• 2.
  You are given 3 statements in symbolic form:
  

  $p$: There is cream in milk
  $q$: There is milk in coffee
  $r$: There is cream in coffee

  a)

  Write the conditional $(p$ ˄ $q)$ $\to$ $r$ in words.
  
  
  b)

  Write the converse$(p$ ˄ $q)$ $\to$ $r$ in words.
  
  
  c)

  Write the biconditional.
  
  

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• 3.
  Truth value of Biconditionals
  Determine the truth value of the following biconditionals:
  a)

  $x = 5$. if and only if $x + 7 = 12$.
  
  
  b)

  If $x > 5$, if and only if $x > 2$.
  
  
  c)

  The triangle is an isosceles, if and only if two sides are equal.
  
  
  d)

  The angle is acute, if and only if the angle is less than 90° degrees.
  
  

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• 4.
  Let both $p$, $q$ and $r$ be statements.
  a)

  If $p$ is true, $q$ is true and $r$ is false, then what is the truth value of the biconditional $(p$ ˄ $q)$ $\leftrightarrow$$r$ ?
  
  
  b)

  If $p$ is false, $q$ is true and $r$ is false, then what is the truth value of the biconditional $(p$ ˄ $q)$ $\leftrightarrow$$r$ ?
  
  
  c)

  If $p$ is false, $q$ is false and $r$ is true, then what is the truth value of the biconditional $(p$ ˄ $q)$ $\leftrightarrow$$r$ ?
  
  
  d)

  If $p$ is false, $q$ is false and $r$ is false, then what is the truth value of the biconditional $(p$ ˄ $q)$ $\leftrightarrow$$r$ ?
  
  

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