How Do Truth Tables and Venn Diagrams Verify Logical Equivalence?

[barbara]

How would I use a truth table to show that the statement p v (q ^ r) is equivalent to (p v q) ^ (p v r) or design a venn diagram for this. and show that this statement is not equivalent to (p v q) ^ r.

 

[Deveno]

A truth-table might begin like this:

$\begin{array}{cccccccc}

P&Q& R&Q\wedge R&P\vee(Q\wedge R)& P\vee Q& P\vee R& (P\vee Q)\wedge(P\vee R)\\
\ast&\ast&\ast&\ast&\ast&\ast&\ast&\ast\\
T&T&T&T&T&T&T&-\\
T&T&F&F&T&T&T&-\\
T&F&T&F&T&T&T&-\\
T&F&F&F&T&T&T&-\\
F&T&T&T&T&T&T&-\\
F&T&F&F&F&T&F&-\\
F&F&T&F&F&F&T&-\\
F&F&F&F&F&F&F&-\\

\end{array}$

Your goal, then, is to fill out column 8, and verify it matches column 5...