SOLUTION: assume P = FALSE, Q = TRUE, and R = FALSE. Determine the truth of the following statements. Problem [q → ~ (r ∨ p)]↔ (p → ~ r ) A. True B. False Pr

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#1
[q → ~ (r ∨ p)]↔ (p → ~ r )
[TRUE → ~ (FALSE ∨ FALSE)]↔ (FALSE → ~ FALSE ) Input given truth values
[TRUE → ~ (FALSE)]↔ (FALSE → TRUE ) Negate the far left truth value and evaluate the disjunction on the right
[TRUE]↔ (TRUE)Evaluate the implications
TRUE
So the answer is A



#2
(~ r ∨ ~ q) ∧ (~ p → r )
(~ FALSE ∨ ~ TRUE) ∧ (~ FALSE → FALSE )Input given truth values
(TRUE ∨ FALSE) ∧ (TRUE → FALSE )Negate
(TRUE) ∧ (FALSE )Evaluate the disjunction and the implication
FALSE
So the answer is B