When the compound proposition is equal to its dual?
Answers
Answer:The dual of a compound proposition that contains only the logical operators of AND (^) ,OR (v) and negation (~) is the compound proposition obtained by replacing each v by ^, each ^ by v, each T by F,and each F by T. The dual of of a compound proposition s is denoted by s*.
so we will have dual s = s* & you can verify it by using truth tables.
For. e.g: p ^ p is equivalent to its dual p v p and as you construct a truth table for those duals, you'll see that both are logically equal. So, s = s* = s.
Similar is for (s*)* = s i.e., as we know that a dual is formed by replacing And with an OR and vice-versa is also possible and same is the case when dealing with T and F .
To be precise, a dual for p v p is p^p i.e., s* is dual of s and again if you apply the duality law for s* again, you'll see that you get back s again i.e.,s = s* = (s*)* = s.
Explanation: