1.) Construct a truth table to determine whether the following sentence is contingent, a contradiction, or a tautology: (A & B) v (B -> A) ANSWER: 2.) Construct a truth table to determine whether the following two sentences are logically equivalent: C -> D D -> C ANSWER: 3.) Construct a truth table to determine whether the following two sentences are consistent: E v ~F F <-> ~E
1.) Construct a truth table to determine whether the following sentence is contingent, a contradiction, or a tautology: (A & B) v (B -> A)
ANSWER:
2.) Construct a truth table to determine whether the following two sentences are logically equivalent:
C -> D
D -> C
ANSWER:
3.) Construct a truth table to determine whether the following two sentences are consistent:
E v ~F
F <-> ~E
ANSWER:
4.) Construct a truth table to determine whether the following sentence is contingent, a contradiction, or a tautology:
G -> ((G v H) & (I v G))
ANSWER:
5.) Construct a truth table to determine whether the following argument is valid:
J -> (K & L)
~(K & L)
∴ ~J & ~L
ANSWER:
The solution of the first three parts is shown below. Please repost the question in the set of three questions for the solution of the remaining parts.
Tautology: If all the resultant values of a statement represented in a truth table are true, then the statement is considered as a tautology statement.
Example:
| A | B | |||
| F | F | T | T | T |
| F | T | T | F | T |
| T | F | F | T | T |
| T | T | T | T | T |
Contradiction: If all the resultant values of a statement represented in a truth table are false, then the statement is considered as a contradiction statement.
Example:
| A | ~A | |
| F | T | F |
| T | F | F |
Contingent: If a statement is neither contradiction nor ati=utology then it is considered as a contingent statement. It has both true and false values.
Example:
| A | B | |
| F | F | F |
| F | T | T |
| T | F | T |
| T | T | T |
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