19. True or False? Use your knowledge of truth tables, classifying statements, a

Question

19. True or False? Use your knowledge of truth tables, classifying statements, and comparing statements to determine which of the following statements are true. Check al that apply. n A pair of propositions can be both logically equivalent and inconsistent n A truth table for the proposition B. P) v (Z. F) requires four rows. n In a truth table for a self-contradictory statement, the column beneath the main operator lists an F on every line. n Two propositions are inconsistent statements if there are no truth table rows in which the statements are true at the same time. n A truth table for a statement with five different simple propositions has 32 rows. n A truth table for the proposition (B. P) v (Z. F) requires 16 rows. nThe conjunction of a self-contradiction and a tautology is a contingent statement. In a truth table for a self-contradiction, the column beneath the main operator lists at least one T and at least one F. If a truth table for multiple statements shows at least one row in which both of the statements have a truth value of F beneath their main operators, then the two statements are logically equivalent. A ruth table for a statement with four simple propostions requires eight rows All self-contradictory statements are logically equivalent to one another. n It is possible for two contingent statements to be inconsistent with one another. n It is possible for two consistent statements to have different actual truth values. nIf a truth table has at least one line in which two statements are false, then the statements are inconsistent statements. n If two statements are inconsistent, they both must be false.

Explanation / Answer

Solution

1. True, as if a pair of proposition is logically equivalent and they may not be logically consistent.

2. False, as number of rows = 2n

3. True, self contradictory have all F's

4. True, no T at the same time

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