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Given the predicate Q(x,y):xy = 1 where x ∈ Z and y ∈ Z. Determine the true values of the following statements. Explain each of your answer 1)∃x Q(1,y) 2)∀x∃y Q(x,y) 3)∃x∀y Q(x,y)

My self-do answer is 1)Yes. For some x as 1, there is a y for x so xy = 1. 2)False. Not for every x there is a y from Z so xy = 1. Counter example: x =2. 3)False. There is not every y for some x so xy = 1. Counter example: x = 2.

Is my understanding and proof correct?

Hanyi Koh
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  • But the question asked me to determine the true values of the statements, so if it is not a statement then how should I get the answer? For question 3, so I cannot use x as counter example but I can use y instead? like y = 3. – Hanyi Koh Oct 15 '19 at 05:03
  • @HanyiKoh $\exists x~Q(1,y)$ is a predicate because $y$ occurs free. Check for typos. – Graham Kemp Oct 25 '19 at 03:50