Am not understanding , how to do the truth or Venn diagram to show a statement pv(q^r)is equivalent to (pvq)^(pvr). How can I show the statement is not equivalent to (pvq)^r.
I have to explain my answer in truth or Venn diagram, but my problem really is Word Problem, and that were I messup at? Please help. I need a step by step of what I'm suppose to do.
By "truth" do you mean a truth table? If so, just list the 8 rows and the 8 values of the functions, and it is easy to show which are equivalent.
To show the equivalence or non-equivalence of two statements in propositional logic using truth tables or Venn diagrams, we can follow a step-by-step process. Let's break it down:
Step 1: Determine the total number of distinct propositions involved in the statement.
In this case, we have three propositions: p, q, and r.
Step 2: Construct the truth table.
Create a truth table with columns for each proposition (p, q, and r) and also for the subexpressions involved in the statement. In this case, we need columns for (q^r), (pvq), (pvr), and (pv(q^r)).
Step 3: Fill in the truth table.
Fill in the truth values for all possible combinations of truth (T) and falsity (F) for the propositions p, q, and r. Also, evaluate the truth values for the subexpressions using the logical connectives (^ and v). Finally, evaluate the truth value for the main statement (pv(q^r)).
Step 4: Compare the truth values.
Look at the columns representing the main statement (pv(q^r)) and the statement (pvq)^(pvr). If the truth values are the same for every row, the statements are equivalent. If there is at least one row where the truth values differ, the statements are not equivalent.
Step 5: Continue with second part of the question.
Now, repeat the same process by creating a new truth table for the statement (pvq)^r. Fill in the truth values for all possible combinations of truth and falsity for the propositions p, q, and r. Evaluate the truth values for the subexpressions (pvq) and (pvq)^r. Compare the truth values for the statement (pvq)^r with the previous main statement and check if they are equivalent or not.
By following these steps, you can determine if the statements are equivalent or not using truth tables. A Venn diagram is generally used to represent sets and their relationships, but it is not typically utilized for evaluating the equivalence of logical statements.