Question

determine whether the statement is true or false. using the dominance of connectives, p → q ∧ r means (p → q) ∧ r. a. the statement is false because the dominance of connectives deals with the grouping of statements, not the placement of parentheses. b. the statement is true because the conjunction has less dominance than the conditional connective. the statement p → q ∧ r means \if p then q, and r\. c. the statement is false because the conditional connective is more dominant than the conjunction connective. the statement p → q ∧ r means \if p, then q and r\. d. the statement is true because a statement is read from left to right and the part of the statement in parentheses is on the left.

Explanation:

In logic, the conditional connective ($\to$) is less dominant than the conjunction connective ($\land$). So, $p\to q\land r$ means $p\to(q\land r)$ and not $(p\to q)\land r$.

Answer:

C. The statement is false because the conjunction connective is more dominant than the conditional connective. The statement $p\to q\land r$ means "if $p$, then $q$ and $r$"