solve this pleaseeeeeee

Asn 2 Friday, October 23, 2020 2:20 AM Problem ( Proving set identities) For any two sets S and T, we define the symmetric difference of S and T, denoted by SAT and defined by SAT=(S\\T)(T\\S). Prove each of the following statements, using only the set identities and proof techniques studied in the lectures. 1. The operation A is associative, that is, for any three sets A,B,C, we have: AA(BAC)=(AAB)AC. 2. For any three sets A,B,C, we have: AUBUC=(AnBNC)U(AnB"NC )(BNC"nA )(CNBinA )(AnBNC )(BnCNA )(CnAnB) 3. For any three sets A, B,C, we have: AA(BAC)=0 - AUBUC=((AnB)\\C)U((AnC)\\B)U((BNC)\\A). Problem ( Foraging in the Forest) In an Autumn foraging group, 150 mycology students were asked to find edible mushrooms. 100 students had found oyster mushrooms, 33 students had found maitake mushrooms, and 23 students had found lion's mane mushrooms. 23 of the students had found both oyster and maitake mushrooms, 12 students had found both maitake and lion's mane mushrooms, 10 students had found both oyster and lion's mane mushrooms and 2 students had found all 3 types of mushrooms. Determine: 1. How many students found only oyster mushrooms? 2. How many students found only maitake mushrooms? 3. How many students found only lion's mane mushrooms? 4. How many students found no mushrooms