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Negation of Statement

Source: 1964 AHSME Problem 12

September 13, 2012
AMC

Problem Statement

Which of the following is the negation of the statement: For all xx of a certain set, x2>0x^2>0?
<spanclass=′latex−bold′>(A)</span> For all x,x2<0 <span class='latex-bold'>(A)</span>\ \text{For all x}, x^2 < 0\qquad <spanclass=′latex−bold′>(B)</span> For all x,x2≤0<span class='latex-bold'>(B)</span>\ \text{For all x}, x^2 \le 0\qquad <spanclass=′latex−bold′>(C)</span> For no x,x2>0<span class='latex-bold'>(C)</span>\ \text{For no x}, x^2>0\qquad <spanclass=′latex−bold′>(D)</span> For some x,x2>0{<span class='latex-bold'>(D)</span>\ \text{For some x}, x^2>0 }\qquad <spanclass=′latex−bold′>(E)</span> For some x,x2≤0{{<span class='latex-bold'>(E)</span>\ \text{For some x}, x^2 \le 0}}
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