Rational and irrational numbers/Pythagorean triple in unit interval/Exercise

a) Give an example of rational numbers ${}a,b,c\in {]0,1[}$ such that

${}a^{2}+b^{2}=c^{2}\,.$

b) Give an example of rational numbers ${}a,b,c\in {]0,1[}$ such that

${}a^{2}+b^{2}\neq c^{2}\,.$

c) Give an example of irrational numbers ${}a,b\in {]0,1[}$ and a rational number ${}c\in {]0,1[}$ such that

${}a^{2}+b^{2}=c^{2}\,.$

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