#6 is isomorphic to De Morgan's laws. Without loss of generality, let the universe be 𝒰 = {0, 1} where S, T ∈ 𝒰. We thereby establish a bijection to boolean logic, and the proof of De Morgan's laws applies.
#3 also looks fun to prove but I'm pretty sure I've done that one before, and LaTeXing out the set operation symbols again might trigger me.
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#6 is isomorphic to De Morgan's laws. Without loss of generality, let the universe be 𝒰 = {0, 1} where S, T ∈ 𝒰. We thereby establish a bijection to boolean logic, and the proof of De Morgan's laws applies.
#3 also looks fun to prove but I'm pretty sure I've done that one before, and LaTeXing out the set operation symbols again might trigger me.
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I like your circumvention of tedium for number 6.
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