IPA FE Subject A sample Question 3
A question IPA Japan published in 基本情報技術者試験 科目A サンプル問題 問3, translated into English. ITPEC is based on the same exams.
Same question on ITPEC: Oct 2024 Q1
P, Q, and R are propositions. It is known that the truth value of proposition P is true, and the values of both the propositions “(not P) or Q” and “(not Q) or R” are true. Which of the following is a combination of the truth values of Q and R? Here, X or Y represents the logical sum of X and Y, and not X represents the negation of X.
Explanation
Q = True, R = True — start from the known value of P and let each true disjunction force the next value.
Since P is true, not P is false, so “(not P) or Q” can be true only if Q is true.
Since Q is true, not Q is false, so “(not Q) or R” can be true only if R is true.
Answer (d)
Why not others:
- •(a) False, False and (b) False, True — with Q false, “(not P) or Q” is false or false = false, breaking the first condition
- •(c) True, False — with Q true and R false, “(not Q) or R” is false or false = false, breaking the second condition
Key rule: “(not X) or Y” is the implication X → Y: when X is true it forces Y to be true, so here the conditions chain P → Q → R.
Basic Theory · AI-written, may contain errors
This question comes from the past questions IPA Japan publishes, translated into English by ITPEC Practice. ITPEC Practice is an independent study tool and is not affiliated with IPA or ITPEC. See the original paper (PDF) or Report an issue.