Question #309691

show in a truth table that p↔q and (p^q) v (¬p^¬q) are logically equivalent.


1
Expert's answer
2022-03-13T18:40:47-0400

Truth table for (pq)(pˉqˉ)(p\wedge q) \vee (\bar p\wedge \bar q) and pqp\leftrightarrow q:

pqpqpˉqˉ(pq)(pˉqˉ)pq000111010000100000111011\begin{vmatrix} p & q & p\wedge q & \bar p\wedge \bar q & (p\wedge q) \vee (\bar p\wedge \bar q) & p\leftrightarrow q\\ 0 & 0 & 0 & 1 & 1 & 1\\ 0 & 1 & 0 & 0 & 0 & 0\\ 1 & 0 & 0 & 0 & 0 & 0\\ 1 & 1 & 1 & 0 & 1 & 1\\ \end{vmatrix}

Since these expressions takes equal values for all p,qp,q, they are logically equivalent.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS