Two or more statements are consistent if it is possible for all of the statements to be true at the same time. If it is impossible for all of the statements to be true at the same time, then the statements are inconsistent. If a truth table for the statements shows that there is at least one row in which the statements are all true together, then the statements are consistent. If there is no row in which the statements are all true together, then the statements are inconsistent. Note that consistent statements are not necessarily actually all true. But if statements are consistent, then it is at least possible for them to be true at the same time. For example, the statement "There is a book on the table" and the statement "There is a cup on the table" may not both be true in actuality, but they are consistent because it is possible for these two statements to be true at the same time. Consistent statements may not have identical truth values in all possible cases (truth table rows). But because each row in a truth table represents a different possible case, the presence of one or more truth table rows in which multiple statements are rue shows that the statements are consistent and that it is possible for the statements to be true at the same time Complete the truth table for the given pair of propositions. Identify the main operator for each proposition by typing a lowercase x in the box beneath the column in which it appears. In the column on the right side of the truth table, indicate ail rows (if there are any) that show consistency with a lowercase X. Proposition A Proposition B (Q v P) (PQ) Truth Table Rows Showing Consistency Given Truth Values Proposition A Proposition B Main Cols.: nconsistent This truth table shows that there which proposition A and proposition B are both true consistent Therefore, proposition A and proposition B are statements