The correct logical equivalence from the following is /are ___ (I) p (q r) (p q) r (II) (p q) r p (q r) (III) (p q) r (p r) ( q r) (IV) p (q r) q (p r)

Step-by-step solution

Using the property A B A B , we evaluate each statement. For (I): p (q r) p ( q r) ( p q) r (p q) r (p q) r Statement (I) is correct. For (II): (p q) r ( p q) r ( p q) r (p q) r (p r) ( q r) p (q r) p q r Statement (II) is incorrect. For (III): (p q) r (p r) ( q r) (p r) ( q r) ( p r) (q r) Statement (III) is incorrect. For (IV): p (q r) p q r q (p r) q ( p r) p q r Statement (IV) is correct. Therefore, only (I) and (IV) are correct. Answer: only (I) and (IV)