Question

Discrete Math

Select the proposition that is a tautology.
a. (pq) → p
b.(p Vq) →p
с. (рлq) ер
d. (paq) →p

Answer 1

The proposition that is a tautology is (p ∧ q) → p. Tautologies are always true, and this proposition is true regardless of the truth values of p and q. Among the given options, this is the only tautology.

Step-by-step explanation:

The proposition that is a tautology is (p ∧ q) → p. A tautology is a proposition that is always true, no matter what the truth values of the variables within it are. Let's evaluate each option:

• (pq) → p: This is a conditional statement and not always true. If p is false and q is true, the antecedent pq is false, and the conditional is false.
• (p V q) → p: This statement is not a tautology because if p is false and q is true, the statement would be false.
• (p ∧ q) → p: This is a tautology, because if p and q are both true, p is certainly true (and if p and q are not both true, the conditional is vacuously true).
• (p ∧ q) → p: This is a repetition of option c and is a tautology as well.

Therefore, the correct answer is option c, which is d in the list of options. (paq) → p is the proposition that represents a tautology as it is always true, regardless of the individual truth values of p and q.