Analytical Ability Reviewer - Part 18

Only 4 of the 32 possible combinations of truth values satisfy all the statements, and the answer holds in every one of them. Each other option can be false in a combination that still satisfies every statement: “If the clinic is closed, then the system is online.” fails when: the system is offline; the council meets in regular session; the applicant passes the interview; the clinic is closed; the budget is approved. “The system is online or the clinic is open (or both).” fails when: the system is offline; the council meets in regular session; the applicant passes the interview; the clinic is closed; the budget is approved. “If the system is offline, then the clinic is closed.” fails when: the system is offline; the council meets in regular session; the applicant passes the interview; the clinic is open; the budget is approved.

“Unless A, B” means “If not A, then B.” Here: If the teacher does not give an assignment, then the pupils do not study at home. The other options reverse or change the condition and are not equivalent.

Only 5 of the 32 possible combinations of truth values satisfy all the statements, and the answer holds in every one of them. Each other option can be false in a combination that still satisfies every statement: “If the budget is approved, then the audit report is submitted.” fails when: the budget is approved; the director is present; the contractor is not accredited; the audit report is not submitted; the road is repaired. “If the budget is approved, then the contractor is accredited.” fails when: the budget is approved; the director is present; the contractor is not accredited; the audit report is not submitted; the road is repaired. “If the budget is approved, then the road is not repaired.” fails when: the budget is approved; the director is present; the contractor is not accredited; the audit report is not submitted; the road is repaired.

Knowing the consequent (the project starts in January) does not prove the antecedent. Affirming the consequent is a fallacy: the project starts in January may happen for other reasons. So the only valid answer is that it cannot be determined whether the budget is approved.

Only 6 of the 32 possible combinations of truth values satisfy all the statements, and the answer holds in every one of them. Each other option can be false in a combination that still satisfies every statement: “If the supplies are delivered, then the evacuation center is opened.” fails when: the supplies are delivered; the permit is not released; the audit report is submitted; the training is conducted; the evacuation center is not opened. “If the evacuation center is not opened, then the permit is not released.” fails when: the supplies are not delivered; the permit is released; the audit report is not submitted; the training is conducted; the evacuation center is not opened. “If the audit report is submitted, then the evacuation center is opened.” fails when: the supplies are delivered; the permit is not released; the audit report is submitted; the training is conducted; the evacuation center is not opened.