Скачать или смотреть GATE CS 2025 | Set 1 | Question: 38 Which of the following predicate logic formulae/formula is/are

GATE CS 2025 | Set 1 | Question: 38
Which of the following predicate logic formulae/formula is/are CORRECT representation(s) of the statement: "Everyone has exactly one mother"?
The meanings of the predicates used are:𝑚𝑜𝑡ℎ𝑒𝑟 (𝑦,𝑥) :𝑦 is the mother of 𝑥 ,𝑛𝑜𝑡𝑒𝑞 (𝑥,𝑦) :𝑥 and 𝑦 are not equal
(A) ∀x∃y∃z(mother(y,x)∧¬mother(z,x))
(B) ∀𝑥∃𝑦[𝑚𝑜𝑡ℎ𝑒𝑟(𝑦,𝑥)∧∀𝑧(𝑛𝑜𝑡𝑒𝑞 (𝑧,𝑦)→¬𝑚𝑜𝑡ℎ𝑒𝑟(𝑧,𝑥) )]
(C) ∀𝑥∀𝑦[𝑚𝑜𝑡ℎ𝑒𝑟(𝑦,𝑥)→∃𝑧(𝑚𝑜𝑡ℎ𝑒𝑟(𝑧,𝑥)∧¬𝑛𝑜𝑡𝑒𝑞(𝑧,𝑦))]
(D) ∀𝑥∃𝑦[𝑚𝑜𝑡ℎ𝑒𝑟(𝑦,𝑥)∧¬∃𝑧(𝑛𝑜𝑡𝑒𝑞(𝑧,𝑦)∧𝑚𝑜𝑡ℎ𝑒𝑟(𝑧,𝑥))]

Ans: (B) & (D)

0:00 Intro & Question
0:37 Solution

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