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Daniel J Smith Custom TMUA Set A Paper 2 · Q7

Paper 2Logic & proof

For real numbers aa and bb, consider the statement S(a,b)S(a,b):

if ab<0ab<0 then a2+b2>0a^2+b^2>0

Which of the following descriptions is correct?

AS(a,b)S(a,b) is false for some real a,ba,b because a2+b2a^2+b^2 can be negative
BS(a,b)S(a,b) is false for some real a,ba,b because a2+b2=0a^2+b^2=0 can occur when ab<0ab<0
CS(a,b)S(a,b) is false for some real a,ba,b because ab<0ab<0 forces a2+b2=0a^2+b^2=0
DS(a,b)S(a,b) is true for all real a,ba,b, and the condition ab<0ab<0 is necessary for a2+b2>0a^2+b^2>0
ES(a,b)S(a,b) is true for all real a,ba,b, and the condition ab<0ab<0 is sufficient and necessary for a2+b2>0a^2+b^2>0
FS(a,b)S(a,b) is true for all real a,ba,b, and the condition ab<0ab<0 is sufficient but not necessary for a2+b2>0a^2+b^2>0
GS(a,b)S(a,b) is true for all real a,ba,b, and the condition ab<0ab<0 is neither necessary nor sufficient for a2+b2>0a^2+b^2>0

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