Question

Using Boolean algebra simplify the statement ¬(𝑟 → 𝑠) → (¬𝑟) 

Answer 1

Using Boolean algebra let us simplify the statement:

$¬(𝑟 → 𝑠) → (¬𝑟) =¬(¬(𝑟 → 𝑠))\lor (¬𝑟) =(𝑟 → 𝑠)\lor (¬𝑟) =(¬𝑟\lor 𝑠)\lor (¬𝑟) = (s\lor ¬𝑟)\lor (¬𝑟) =s\lor( ¬𝑟\lor ¬𝑟) =s\lor ¬𝑟=¬𝑟\lor s=𝑟 → 𝑠.$