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?