sentence1: How can it be proven that -LSB- math -RSB- x + y = x \ times y = \ frac -LCB- x -RCB- -LCB- y -RCB- -LSB- / math -RSB- ?
sentence2: Set Theory : How do we prove , rigorously , that if -LSB- math -RSB- X \ subseteq Y -LSB- / math -RSB- , then -LSB- math -RSB- X \ cup Y = Y -LSB- / math -RSB- -- and the same for the case -LSB- math -RSB- X \ cap Y = X -LSB- / math -RSB- ?