Two propositions are logically equivalent statements if their truth tables have
ID: 3011223 • Letter: T
Question
Two propositions are logically equivalent statements if their truth tables have the same truth values on each row under their main operators. If two statements are not logically equivalent, then they must be contradictory. It is possible for two contingent statements to be contradictory to one another. A truth table for a statement with three simple propositions requires six rows. If a truth table for multiple statements shows at least one row in which both of the statements have a truth value of true beneath their main operators, then the two statements are logically equivalent. In a truth table for a contingent statement, the column beneath the main operator lists a T on every line. A truth table for a statement with only one simple proposition requires two rows. All contingent statements are logically equivalent to one another. All tautologies are true statements. A truth table for the proposition (~Z v ~F) d ~(C = F) requires eight rows. Some pairs of self-contradictory statements are consistent with each other. In a truth table for a tautology, the column beneath the main operator lists a T on every line. A truth table for the proposition Z middot ~F requires two rows. It is possible for two statements to be false but consistent with one another. A statement cannot be both a tautology and a self-contradiction.Explanation / Answer
1) True. It is well known fact.
2) False. Two statements which are not equivalent "can be" contradictory, but is it not necessarily true. For example, Statement 1: It rained last week. Statement 2: It rained last friday. These two statements are not equivalent, but they not contradictory either. Therefore, the statement is false.
3) True.
4) False. Number of rows must be equal to 2^3 = 8
5) False. Just one row is not sufficient. It must hold for all the rows for two statements to be equivalent.
6) False. A statement is only contingent if it contains both T and F in the column of its main operator.
7) True. The number of rows = 2^1 = 2.
8) False. Not necessarily, but it can be true in some cases.
9) True. This is a well known fact.
10) True. Since we have three propositions, therefore, number of rows = 2^3 = 8
11) False. For a pair of statements to be consistent, they both must be true, which is not the case in self contraditory statements.
12) True.
13) False. Because we have two variables, so number of rows in the truth table will be 2^2 = 4
14) False. In order to be consistent, both the statements must be true.
15) True.
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