1. Other
  2. Other
  3. problem 112 demorgans laws let a and b be statements...

Question: problem 112 demorgans laws let a and b be statements...

Question details

PROBLEM 1.12 (DeMorgans Laws). Let A and B be statements and establish the followring 1. ~(A A B) is logically equivalent to (~ A) VB) 2. (AV B) is logically equivalent to ( A) A(B Before we move on to other logical connectives well collect a few algebraic properties of the connectives we already have. Problem 1.13 (The Commutative Property). Prove each of the following 1. A^ B is logically equivalent to B^A 2. Av Bis logically equivalent to BvA Problem 1.14 (The Associative Property). Prove each of the following 1. (А Л B) ^ C is logically equivalent to A ^ (B ^ C) 2. (A v B) v C is logically equivalent to A v (B v C) Problem 1.15 (The Distributive Property). Prove each of the following: 1. AA (BVC) is logically equivalent to (AAB)V(AAC) 2. Av (BAC) is logically equivalent to (AV B)A(AVC) Problem 1.16. Prove each of the following: 1. А Л (В Л C) is logically equivalent to (A ^ BA (A ЛС) 2. Av (BvC) is logically equivalent to (AVB)V (AvC) 1.3 Implications Now well examine compound statements of the forim if A, then B. In this statement the if A part is called the antecedent or hypothesis and A is called the sufficient condition for the
Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution