Question

Type the correct answer in each box. use t for true and f for false. complete the truth table for the inverse of a conditional statement. pq ttt tff ftt fft

Answer 1

The task was to complete a truth table for the inverse of a conditional statement. The inverse inverts both the hypothesis and the conclusion's truth values.

Step-by-step explanation:

The question is related to constructing a truth table for the inverse of a conditional statement. Conditional statements often take the form of 'if p then q.' The inverse of this statement is 'if not p then not q.' Writing the truth values for the inverse requires flipping the truth values for both p and q. Given a truth table of the form pq, with T for true and F for false, we can complete the truth table for the inverse as follows:

• p: T, q: T, inverse: F F
• p: T, q: F, inverse: F T
• p: F, q: T, inverse: T F
• p: F, q: F, inverse: T T

The table shows that each original pair of p and q is inverted, providing the truth value for the inverse conditional statement.

The complete question is:content loaded

Type the correct answer in each box. use t for true and f for false. complete the truth table for the inverse of a conditional statement. pq ttt tff ftt fft is:

Answer 2

The truth table for the inverse of a conditional statement (If not P then not Q) with given conditions PQ TTT TFF FTT FFT will have the truth values True, True, False, and True respectively for each row.

Step-by-step explanation:

To complete the truth table for the inverse of a conditional statement, we have to understand what the inverse of a conditional statement is.

A conditional statement is typically written in the form 'If P then Q', often referred as 'P implies Q'. The inverse of this statement is 'If not P then not Q'. Let's consider P to be the hypothesis and Q to be the conclusion.

The truth table for an inverse conditional statement has two columns for the original statements P and Q and then a separate column for the inverse 'not P implies not Q'.

The given problem provides us with the truth table values: PQ TTT TFF FTT FFT. To evaluate this, we will look at each row and determine the truth value for 'not P implies not Q'.

1. For the first given condition (P=true, Q=true), the inverse would be 'not P=false, not Q=false', which means 'false implies false'. This statement is true, because an implication with a false premise is always true.
2. For the second condition (P=true, Q=false), the inverse would be 'not P=false, not Q=true', which means 'false implies true', which is also true.
3. For the third condition (P=false, Q=true), the inverse is 'not P=true, not Q=false', meaning 'true implies false', which is false.
4. For the last condition (P=false, Q=false), the inverse is 'not P=true, not Q=true', which is 'true implies true', and thus true.