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Rest, determine the negation, converse, and contrapositive of the given quantifier statement. We have for every number X, if the absolute value of X is less than 1, then X squared is less than 1. Lets assume the implication in the parenthesis is in the form of if P then Q, where P the hypothesis is the absolute value of X is less than 1, and Q the conclusion is X squared is less than 1. Number one, were asked to state the negation. We begin by negating this statement from here and now we simplify. The negation passes across the quantifier changing the quantifier type, and then we negate the implication. So again, for the first step, the negation passes across the quantifier, the quantifier changes from for every X to their existing X, and now we negate the implication. The negation of the implication of P then Q is logically equivalent to P and the not-Q. The negation of if the absolute of X less than 1, then X squared less than 1, is absolute value of X less than 1 and X squared gre
