Discrete Math Question - Truth Tables and Equivalences

Use equivalences to show: ~B ^(A -> B) = ~(B v A) (I used ~ to mean "not") I am confused on which laws to apply. (De Morgan, Distribution, Conversion or absorption) Also, I do not fully understand the concept of the problem and how to work it. Our teacher has given us three problems: 1. B ^(A -> B) = (B v A) 2. (A v B) -> C = (A -> C) ^ (B -> C) 3. A -> (B v C) = (A -> B) v (A -> C) Can you help me work one of the problems to help get me started.

Discrete mathematics

List 16 different relations on the set {0,1} as sets of pairs. State if they are reflexive, transitive, symmetric, antisymmetric

Discrete mathematics

Let R be a symmetric relation show that R to the power n is symmetric for all positive integers n.

Discrete mathematics

Show that the symmetric closure of the union of 2 relations is the union of their symmetric closures.

Discrete mathematics

A relation R is called circular if a R b and b R c imply that c R a. Show that R is reflexive and circular if and only if it is an equivalence relation.