Rewriting biconditional statements into conditional statement without arrows (discrete math)I'm stuck on rewriting biconditional statements to conditional statements without using arrows. the original is as follows: ( ( P → ( ∼ Q ) ) ↔ r ) and what i (believe) the correct answer is: ( ( ∼ P V ∼ Q ) ↔ r ) [ ∼ ( ∼ P V ∼ Q ) V r ] Λ [ ( ∼ r V ( ∼ P V ∼ Q ) ]If anyone would like to correct and explain why i'm wrong or verify it's correct I would greatly appreciate it.

Question

Rewriting biconditional statements into conditional statement without arrows (discrete math)I&#039;m stuck on rewriting biconditional statements to conditional statements without using arrows. the original is as follows:  (  (  P  →  (  ∼  Q  )  )  ↔  r  ) and what i (believe) the correct answer is:  (  (  ∼  P  V  ∼  Q  )  ↔  r  )  [  ∼  (  ∼  P  V  ∼  Q  )  V  r  ]      Λ    [  (  ∼  r  V  (  ∼  P  V  ∼  Q  )  ]If anyone would like to correct and explain why i&#039;m wrong or verify it&#039;s correct I would greatly appreciate it.

Sandra Randall · Accepted Answer

Step 1Statement   A  ⇒  B can be reduced to   B  ∨              A      ¯      And   P    ⟺    Q is equivalent to   (  P  ⇒  Q  )  ∧  (  Q  ⇒  P  )Step 2So,   (  (  P  ⇒            Q      ¯        )    ⟺    r  ) is equivalent to-             Q      ¯          ∨            P      ¯          ⟺    r-   (  r  ∨                              Q          ¯                          ∨                        P          ¯                      ¯    )  ∧  (  (            Q      ¯          ∨            P      ¯        )  ∨            r      ¯        )So I think your answer is correct.