An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
p ∨ q (p or q) is true if either p or q (or both) are true, and false otherwise.
p ∧ q (p and q) is true if both p and q are true, and false otherwise.
Fill in the truth values for p ∨ q and p ∧ q based on the truth values of p and q .
The completed truth table is:
p
q
p \vee q
p \wedge q
T
T
T
T
T
F
T
F
F
T
T
F
F
F
F
F
Explanation
Understanding the Problem We are given a truth table with statements p and q , and we need to complete the columns for p ∨ q (p or q) and p ∧ q (p and q).
Understanding OR Recall that p ∨ q is true if either p or q (or both) is true, and false otherwise.
Understanding AND Recall that p ∧ q is true if both p and q are true, and false otherwise.
Row 1: T and T For the first row, p is true and q is true. Thus, p ∨ q is true and p ∧ q is true.
Row 2: T and F For the second row, p is true and q is false. Thus, p ∨ q is true and p ∧ q is false.
Row 3: F and T For the third row, p is false and q is true. Thus, p ∨ q is true and p ∧ q is false.
Row 4: F and F For the fourth row, p is false and q is false. Thus, p ∨ q is false and p ∧ q is false.
Completed Truth Table Therefore, the completed truth table is:
p
q
p \vee q
p \wedge q
T
T
T
T
T
F
T
F
F
T
T
F
F
F
F
F
Examples
Truth tables are used in computer science to design digital circuits and in mathematics to prove logical statements. For example, when designing a digital circuit, engineers use truth tables to define the behavior of logic gates like AND, OR, and NOT gates. These gates are the building blocks of more complex circuits. Understanding truth tables helps in simplifying complex logical expressions and optimizing circuit designs, ensuring efficient and reliable operation of electronic devices.
