The sentence "P → Q" is read as (3)
P or Q
P and Q
If P then Q
Q if and only P
2. In the truth table for an invalid argument, (2)
on at least one row, where the premises are all true, the conclusion is true.
on at least one row, where the premises are all true, the conclusion is false.
on all the rows where the premises are all true, the conclusion is true.
on most of the rows, where the premises are all true, the conclusion is true.
3. Truth tables can (1 0R 2)
display all the possible truth values involved with a set of sentences.
determine what scientific claims are true.
determine if inductive arguments are strong.
determine if inductive arguments are weak.
4. Truth tables can determine which of the following? (1)
If an argument is valid
If an argument is sound
If a sentence is valid
All of the above
5. If P is false, and Q is false, the truth-value of "P ↔Q" is (1)
false.
true.
Cannot be determined.
All of the above.
6. What is the truth value of the sentence "P v ~ P"? (Points : 1)
True
False
Cannot be determined
Not a sentence
7. If P is true, and Q is false, the truth-value of "P v Q" is (1)
false.
true.
Cannot be determined
All of the above
8. The sentence "P ↔ Q" is best read as
(4)
If P then Q
If Q then P
P or Q
P if and only if Q
9. What is the truth value of the sentence "P & ~ P"? (3)
True
False
Cannot be determined
Not a sentence
10. In the conditional "P →Q," "P" is a (3)
sufficient condition for Q.
sufficient condition for P.
necessary condition for P.
necessary condition for Q.
We won't do your homework here, what are your answers?
It's in the brackets with numbers
1. The sentence "P → Q" is read as (3) "If P then Q." To understand this, we can break it down as follows: P represents the premise or condition, and Q represents the conclusion or result. So, the sentence "P → Q" means that if P is true, then Q must be true as well.
2. In the truth table for an invalid argument, (2) on at least one row, where the premises are all true, the conclusion is false. To determine whether an argument is valid or invalid, we construct a truth table. If there is at least one row in the truth table where all the premises are true but the conclusion is false, then the argument is invalid.
3. Truth tables can (1 OR 2) display all the possible truth values involved with a set of sentences. One of the main uses of truth tables is to display all the possible combinations of truth values for a set of sentences or logical expressions. This helps us understand the truth values of complex expressions and evaluate their validity.
4. Truth tables can determine which of the following? (1) If an argument is valid, (2) If an argument is sound, (3) If a sentence is valid, (4) All of the above. Truth tables can determine if an argument is valid by checking if there is no row in the truth table where all the premises are true and the conclusion is false. However, truth tables cannot determine if an argument is sound as soundness requires both validity and all true premises.
5. If P is false, and Q is false, the truth-value of "P ↔ Q" is (1) false. The truth value of the biconditional "P ↔ Q" is false if both P and Q have different truth values. In this case, since both P and Q are false, the biconditional is false.
6. The truth value of the sentence "P v ~ P" is (1) true. The sentence "P v ~ P" represents the logical expression of a disjunction ("or") between P and its negation (~P). In a disjunction, if at least one of the disjuncts is true, the whole expression is true. In this case, since one of either P or its negation ~P must be true, the expression will always evaluate to true.
7. If P is true, and Q is false, the truth-value of "P v Q" is (1) true. The sentence "P v Q" represents the logical expression of a disjunction ("or") between P and Q. In a disjunction, if at least one of the disjuncts is true, the whole expression is true. In this case, since P is true, the whole expression is true regardless of the truth value of Q.
8. The sentence "P ↔ Q" is best read as (4) "P if and only if Q." The biconditional "P ↔ Q" represents a statement that is true if and only if both P and Q have the same truth values. It can be read as "P if and only if Q" to emphasize the mutual dependence of P and Q.
9. The truth value of the sentence "P & ~ P" is (2) false. The sentence "P & ~ P" represents the logical expression of a conjunction ("and") between P and its negation (~P). In a conjunction, both conjuncts must be true for the whole expression to be true. However, since P and its negation ~P have opposite truth values, the conjunction will always evaluate to false.
10. In the conditional "P → Q," "P" is a (3) necessary condition for P. In a conditional statement "P → Q," P is considered a necessary condition for Q. It means that if P is true, then Q must also be true. However, if P is false, it does not necessarily imply that Q is false.