we can also do it by solving equations.
I) p^2 < 2p. This means p^2 - 2p < 0 or p(p-2) < 0.. this will be true for 0<p<2. Since this range is within our given range (1<p<3), this statement COULD be true. Eg for p=1
II) p^2 = 2p. This means p^2 - 2p = 0 or p(p-2) = 0.. this will be true for p=0 and p=2. Since p=2 lies within the given range (1<p<3), this statement COULD be true. for p=2
III) p^2 > 2p. This means p^2 - 2p > 0 or p(p-2) > 0.. this will be true
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I) p^2 < 2p. This means p^2 - 2p < 0 or p(p-2) < 0.. this will be true for 0<p<2. Since this range is within our given range (1<p<3), this statement COULD be true. Eg for p=1
II) p^2 = 2p. This means p^2 - 2p = 0 or p(p-2) = 0.. this will be true for p=0 and p=2. Since p=2 lies within the given range (1<p<3), this statement COULD be true. for p=2
III) p^2 > 2p. This means p^2 - 2p > 0 or p(p-2) > 0.. this will be true
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