Question

10. Comparing Statements - Practice 2

Complete the truth table for the given propositions. Indicate each proposition's main operator by typing a lowercase x in box beneath the column in which it appears. On the right side of the truth table, indicate whether each row lists identical or opposite truth values for the two statements. Also indicate which, if any, rows show that the statements are consistent with a lowercase x. Finally, answer the questions beneath the truth table about the classification for each proposition and the relation between the two propositions.

Proposition A	Proposition B
C ⊃ ~(D ⊃ E)	~(D ⊃ E) ∨ ~C

Given Truth Values				Truth Table																		Truth Values	Rows Showing Consistency
				Proposition A									Proposition B
C	D	E		C	⊃	~	(	D	⊃	E	)	/	~	(	D	⊃	E	)	∨	~	C
T	T	T
T	T	F
T	F	T
T	F	F
F	T	T
F	T	F
F	F	T
F	F	F
			Main Cols.:

According to the truth table, what type of statement is proposition A?

Contingent statement

Self-contradictory statement

Tautology

According to the truth table, what type of statement is proposition B?

Self-contradictory statement

Contingent statement

Tautology

Are proposition A and proposition B logically equivalent statements, contradictory statements, or neither?

Neither logically equivalent nor contradictory statements

Contradictory statements

Logically equivalent statements

Are proposition A and proposition B consistent statements or inconsistent statements?

Inconsistent statements

Consistent statements

Answer 1