ITPEC FE Subject A October 2024 Question 1
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
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