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in this problem weamp;#39;re going to investigate a whole bunch of statements and determine if these statements are true or false statements we worked problems like this before the difference with these statements is they involve the quantifiers that weamp;#39;ve been investigating things like for all and their exist so here in part A letamp;#39;s look at this statement for all X there exist a y such that x - y equal 0 and the question we need to answer is is this a true or false statement well obviously this is a true statement and thatamp;#39;s easy to think about for any x that you want to pick from the natural numbers whether thatamp;#39;s 0 1 2 3 4 letamp;#39;s just say x is 4 is there a value y does there exist a y also in the natural numbers such that their difference is zero and there obviously does when X is 4 I can choose y equal to 4 which is in the natural numbers and then 4 - 4 = Z and then I can do that no matter what value of x is picked so for all X I would choose
