Question

In Exercises 1 to 10, determine the truth value of the compound statement given that p is a false statement, q is a true statement, and r is a true statement. 1. PV (~qVr) 2. rA ~(pVr) 4. (pAq)V[(~pA~q) Va] 5. [~(pA~q) Vr]^(pA~r) 6. (pA~q)V[(pA~q) Vr] 7. [(pA~q)V~r]^(gAr) 8. （~p^g）^［（pA~9）Vr］ 9.［（p/q） Ar］VIpv（g^→）］

Answer 1

To determine the truth value of given compound statements, one must analyze each component considering the logical operators and the given truth values of the individual statements p, q, and r.

Step-by-step explanation:

The question pertains to determining the truth value of compound statements given the truth values of individual statements. Since we are given that statement p is false, q is true, and r is true, the truth value of each compound statement needs to be assessed based on these premises.

For example, to evaluate the compound statement p V (~q V r), first evaluate the truth value of each component within the parentheses considering the logical operators. The use of 'V' denotes the logical OR operator, and '~' represents the logical negation. After evaluating the components, the final truth value of the entire compound statement can be determined.

As another example for statement 2, r A ~(p V r), you would individually check the truth value of ~(p V r) first and then use the conjunction operator 'A', which stands for logical AND, to find the truth value for the entire expression.